%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : LCL763-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n016.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 : Mon Sep 7 12:21:55 PM UTC 2026
% Result : Unsatisfiable 7.64s 8.01s
% Output : CNFRefutation 7.64s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named inputERROR: Could not build tree for root to_be_clausified_0ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)),
input ).
fof(cls_ATP__Linkup_Oequal__imp__fequal_0_0,plain,
! [T_a,V_x] :
( hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0]) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
input ).
fof(clsarity_bool__Orderings_Oorder_0,plain,
( class_Orderings_Oorder(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Oorder]) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
input ).
fof(clsarity_bool__Orderings_Opreorder_0,plain,
( class_Orderings_Opreorder(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Opreorder]) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Oorder_0,plain,
( class_Orderings_Oorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Oorder]) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Olinorder_0,plain,
( class_Orderings_Olinorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Olinorder]) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Opreorder_0,plain,
( class_Orderings_Opreorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Opreorder]) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Omonoid__add_0,plain,
( class_OrderedGroup_Omonoid__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add]) ).
cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Osemigroup__add_0,plain,
( class_OrderedGroup_Osemigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Osemigroup__add]) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Ocomm__monoid__add_0,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__add]) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Oab__semigroup__add_0,plain,
( class_OrderedGroup_Oab__semigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__add]) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Ocomm__semiring__1_0,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1]) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Oordered__semidom_0,plain,
( class_Ring__and__Field_Oordered__semidom(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom]) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Ocancel__semigroup__add_0,plain,
( class_OrderedGroup_Ocancel__semigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__semigroup__add]) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add_0,plain,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add]) ).
cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add_0,plain,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__comm__monoid__add]) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le]) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add_0,plain,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add]) ).
cnf(cls_dB_Osimps_I5_J_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
input ).
fof(cls_dB_Osimps_I5_J_0_0,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I5_J_0]) ).
cnf(cls_Var__eq__apps__conv_2,axiom,
c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_Var__eq__apps__conv_2_0,plain,
! [V_m] :
( c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_Var__eq__apps__conv_2]) ).
cnf(cls_foldl__Nil_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a,
input ).
fof(cls_foldl__Nil_0_0,plain,
! [T_a,T_b,V_a,V_f] :
( c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a
| $false ),
inference(orientation,[status(thm)],[cls_foldl__Nil_0]) ).
cnf(cls_dB_Osimps_I4_J_0,axiom,
c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H),
input ).
fof(cls_dB_Osimps_I4_J_0_0,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I4_J_0]) ).
cnf(cls_App__eq__foldl__conv_4,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_App__eq__foldl__conv_4_0,plain,
! [V_r,V_s] :
( hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_App__eq__foldl__conv_4]) ).
cnf(cls_apps__eq__Abs__conv_2,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r),
input ).
fof(cls_apps__eq__Abs__conv_2_0,plain,
! [V_r] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r)
| $false ),
inference(orientation,[status(thm)],[cls_apps__eq__Abs__conv_2]) ).
cnf(cls_Abs__eq__apps__conv_2,axiom,
c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_Abs__eq__apps__conv_2_0,plain,
! [V_r] :
( c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_Abs__eq__apps__conv_2]) ).
cnf(cls_Abs__App__neq__Var__apps_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_Abs__App__neq__Var__apps_0_0,plain,
! [V_n,V_s,V_ss,V_t] :
( hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_Abs__App__neq__Var__apps_0]) ).
cnf(cls_Var__apps__neq__Abs__apps_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_Var__apps__neq__Abs__apps_0_0,plain,
! [V_n,V_r,V_ss,V_ts] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_Var__apps__neq__Abs__apps_0]) ).
cnf(cls_app__last_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u) = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_ts,c_List_Olist_OCons(V_u,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_app__last_0_0,plain,
! [V_t,V_ts,V_u] :
( hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u) = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_ts,c_List_Olist_OCons(V_u,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_app__last_0]) ).
cnf(cls_typing_OVar_0,axiom,
c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)),
input ).
fof(cls_typing_OVar_0_0,plain,
! [V_env,V_x] :
( c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x))
| $false ),
inference(orientation,[status(thm)],[cls_typing_OVar_0]) ).
cnf(cls_dB_Osimps_I10_J_0,axiom,
c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat),
input ).
fof(cls_dB_Osimps_I10_J_0_0,plain,
! [T_a,V_f1,V_f2,V_f3,V_nat] :
( c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I10_J_0]) ).
cnf(cls_dB_Osimps_I6_J_0,axiom,
c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
input ).
fof(cls_dB_Osimps_I6_J_0_0,plain,
! [V_dB_H,V_nat] :
( c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I6_J_0]) ).
cnf(cls_dB_Orecs_I1_J_0,axiom,
c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat),
input ).
fof(cls_dB_Orecs_I1_J_0_0,plain,
! [T_a,V_f1,V_f2,V_f3,V_nat] :
( c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Orecs_I1_J_0]) ).
cnf(cls_beta__cases_I1_J_0,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
input ).
fof(cls_beta__cases_I1_J_0_0,plain,
! [V_i,V_t] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t))
| $false ),
inference(orientation,[status(thm)],[cls_beta__cases_I1_J_0]) ).
cnf(cls_subst__eq_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u,
input ).
fof(cls_subst__eq_0_0,plain,
! [V_k,V_u] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u
| $false ),
inference(orientation,[status(thm)],[cls_subst__eq_0]) ).
cnf(cls_dB_Osimps_I7_J_0,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
input ).
fof(cls_dB_Osimps_I7_J_0_0,plain,
! [V_dB_H,V_nat] :
( c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I7_J_0]) ).
cnf(cls_foldl__append_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b),
input ).
fof(cls_foldl__append_0_0,plain,
! [T_a,T_b,V_a,V_f,V_xs,V_ys] :
( c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_foldl__append_0]) ).
cnf(cls_foldl__Cons_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b),
input ).
fof(cls_foldl__Cons_0_0,plain,
! [T_a,T_b,V_a,V_f,V_x,V_xs] :
( c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_foldl__Cons_0]) ).
cnf(cls_ex__head__tail_0,axiom,
V_t = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(V_t),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(V_t),tc_Lambda_OdB,tc_Lambda_OdB),
input ).
fof(cls_ex__head__tail_0_0,plain,
! [V_t] :
( V_t = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(V_t),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(V_t),tc_Lambda_OdB,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_ex__head__tail_0]) ).
cnf(cls_substn_Osimps_I2_J_0,axiom,
c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k)),
input ).
fof(cls_substn_Osimps_I2_J_0_0,plain,
! [V_k,V_s,V_t,V_u] :
( c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k))
| $false ),
inference(orientation,[status(thm)],[cls_substn_Osimps_I2_J_0]) ).
cnf(cls_liftn_Osimps_I2_J_0,axiom,
c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k)),
input ).
fof(cls_liftn_Osimps_I2_J_0_0,plain,
! [V_k,V_n,V_s,V_t] :
( c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k))
| $false ),
inference(orientation,[status(thm)],[cls_liftn_Osimps_I2_J_0]) ).
cnf(cls_dB_Orecs_I2_J_0,axiom,
c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a)),
input ).
fof(cls_dB_Orecs_I2_J_0_0,plain,
! [T_a,V_dB1,V_dB2,V_f1,V_f2,V_f3] :
( c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_dB_Orecs_I2_J_0]) ).
cnf(cls_dB_Osimps_I11_J_0,axiom,
c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(V_f2,V_dB1),V_dB2),
input ).
fof(cls_dB_Osimps_I11_J_0_0,plain,
! [T_a,V_dB1,V_dB2,V_f1,V_f2,V_f3] :
( c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(V_f2,V_dB1),V_dB2)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I11_J_0]) ).
cnf(cls_lift_Osimps_I2_J_0,axiom,
c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(V_s,V_k)),c_Lambda_Olift(V_t,V_k)),
input ).
fof(cls_lift_Osimps_I2_J_0_0,plain,
! [V_k,V_s,V_t] :
( c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(V_s,V_k)),c_Lambda_Olift(V_t,V_k))
| $false ),
inference(orientation,[status(thm)],[cls_lift_Osimps_I2_J_0]) ).
cnf(cls_dB_Osimps_I9_J_0,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),
input ).
fof(cls_dB_Osimps_I9_J_0_0,plain,
! [V_dB1,V_dB2,V_dB_H] :
( c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I9_J_0]) ).
cnf(cls_dB_Osimps_I8_J_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
input ).
fof(cls_dB_Osimps_I8_J_0_0,plain,
! [V_dB1,V_dB2,V_dB_H] :
( hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I8_J_0]) ).
cnf(cls_subst__App_0,axiom,
c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_t,V_s,V_k)),c_Lambda_Osubst(V_u,V_s,V_k)),
input ).
fof(cls_subst__App_0_0,plain,
! [V_k,V_s,V_t,V_u] :
( c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_t,V_s,V_k)),c_Lambda_Osubst(V_u,V_s,V_k))
| $false ),
inference(orientation,[status(thm)],[cls_subst__App_0]) ).
cnf(cls_rev__is__Nil__conv_1,axiom,
c_List_Orev(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_rev__is__Nil__conv_1_0,plain,
! [T_a] :
( c_List_Orev(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rev__is__Nil__conv_1]) ).
cnf(cls_listrelp_ONil_0,axiom,
c_List_Olistrelp(V_r,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a),
input ).
fof(cls_listrelp_ONil_0_0,plain,
! [T_a,V_r] :
( c_List_Olistrelp(V_r,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_listrelp_ONil_0]) ).
cnf(cls_Nil__is__append__conv_2,axiom,
c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a),
input ).
fof(cls_Nil__is__append__conv_2_0,plain,
! [T_a] :
( c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Nil__is__append__conv_2]) ).
cnf(cls_Nil__is__map__conv_1,axiom,
c_List_Olist_ONil(T_a) = c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a),
input ).
fof(cls_Nil__is__map__conv_1_0,plain,
! [T_a,T_b,V_f] :
( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Nil__is__map__conv_1]) ).
cnf(cls_rotate__is__Nil__conv_1,axiom,
c_List_Orotate(V_n,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_rotate__is__Nil__conv_1_0,plain,
! [T_a,V_n] :
( c_List_Orotate(V_n,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rotate__is__Nil__conv_1]) ).
cnf(cls_list_Osimps_I4_J_0,axiom,
c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_ONil(T_b),T_a,T_b) = V_f1,
input ).
fof(cls_list_Osimps_I4_J_0_0,plain,
! [T_a,T_b,V_f1,V_f2] :
( c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_ONil(T_b),T_a,T_b) = V_f1
| $false ),
inference(orientation,[status(thm)],[cls_list_Osimps_I4_J_0]) ).
cnf(cls_map__upds__Nil1_0,axiom,
c_Map_Omap__upds(V_m,c_List_Olist_ONil(T_a),V_bs,T_a,T_b) = V_m,
input ).
fof(cls_map__upds__Nil1_0_0,plain,
! [T_a,T_b,V_bs,V_m] :
( c_Map_Omap__upds(V_m,c_List_Olist_ONil(T_a),V_bs,T_a,T_b) = V_m
| $false ),
inference(orientation,[status(thm)],[cls_map__upds__Nil1_0]) ).
cnf(cls_map__upds__Nil2_0,axiom,
c_Map_Omap__upds(V_m,V_as,c_List_Olist_ONil(T_b),T_a,T_b) = V_m,
input ).
fof(cls_map__upds__Nil2_0_0,plain,
! [T_a,T_b,V_as,V_m] :
( c_Map_Omap__upds(V_m,V_as,c_List_Olist_ONil(T_b),T_a,T_b) = V_m
| $false ),
inference(orientation,[status(thm)],[cls_map__upds__Nil2_0]) ).
cnf(cls_remove1_Osimps_I1_J_0,axiom,
c_List_Oremove1(V_x,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_remove1_Osimps_I1_J_0_0,plain,
! [T_a,V_x] :
( c_List_Oremove1(V_x,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_remove1_Osimps_I1_J_0]) ).
cnf(cls_list_Osimps_I3_J_0,axiom,
c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a),
input ).
fof(cls_list_Osimps_I3_J_0_0,plain,
! [T_a,V_a_H,V_list_H] :
( c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_list_Osimps_I3_J_0]) ).
cnf(cls_neq__Nil__conv_1,axiom,
c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a),
input ).
fof(cls_neq__Nil__conv_1_0,plain,
! [T_a,V_x,V_xa] :
( c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_neq__Nil__conv_1]) ).
cnf(cls_list__update_Osimps_I1_J_0,axiom,
c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_v,T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_list__update_Osimps_I1_J_0_0,plain,
! [T_a,V_i,V_v] :
( c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_v,T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_list__update_Osimps_I1_J_0]) ).
cnf(cls_list__update__code_I1_J_0,axiom,
c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_y,T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_list__update__code_I1_J_0_0,plain,
! [T_a,V_i,V_y] :
( c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_y,T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_list__update__code_I1_J_0]) ).
cnf(cls_list__update__nonempty_1,axiom,
c_List_Olist__update(c_List_Olist_ONil(T_a),V_k,V_x,T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_list__update__nonempty_1_0,plain,
! [T_a,V_k,V_x] :
( c_List_Olist__update(c_List_Olist_ONil(T_a),V_k,V_x,T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_list__update__nonempty_1]) ).
cnf(cls_filter_Osimps_I1_J_0,axiom,
c_List_Ofilter(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_filter_Osimps_I1_J_0_0,plain,
! [T_a,V_P] :
( c_List_Ofilter(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_filter_Osimps_I1_J_0]) ).
cnf(cls_filtermap_Osimps_I1_J_0,axiom,
c_List_Ofiltermap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_filtermap_Osimps_I1_J_0_0,plain,
! [T_a,T_b,V_f] :
( c_List_Ofiltermap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_filtermap_Osimps_I1_J_0]) ).
cnf(cls_append__eq__append__conv2_5,axiom,
c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a),
input ).
fof(cls_append__eq__append__conv2_5_0,plain,
! [T_a,V_ts,V_x,V_xs] :
( c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__eq__append__conv2_5]) ).
cnf(cls_append__eq__append__conv2_4,axiom,
c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a) = c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a),
input ).
fof(cls_append__eq__append__conv2_4_0,plain,
! [T_a,V_x,V_ys,V_zs] :
( c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a) = c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__eq__append__conv2_4]) ).
cnf(cls_append__eq__appendI_0,axiom,
c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a),
input ).
fof(cls_append__eq__appendI_0_0,plain,
! [T_a,V_us,V_xs,V_xs1] :
( c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__eq__appendI_0]) ).
cnf(cls_append__assoc_0,axiom,
c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a) = c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a),
input ).
fof(cls_append__assoc_0_0,plain,
! [T_a,V_xs,V_ys,V_zs] :
( c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a) = c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__assoc_0]) ).
cnf(cls_list__update__overwrite_0,axiom,
c_List_Olist__update(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_i,V_y,T_a) = c_List_Olist__update(V_xs,V_i,V_y,T_a),
input ).
fof(cls_list__update__overwrite_0_0,plain,
! [T_a,V_i,V_x,V_xs,V_y] :
( c_List_Olist__update(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_i,V_y,T_a) = c_List_Olist__update(V_xs,V_i,V_y,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_list__update__overwrite_0]) ).
cnf(cls_rev__filter_0,axiom,
c_List_Orev(c_List_Ofilter(V_P,V_xs,T_a),T_a) = c_List_Ofilter(V_P,c_List_Orev(V_xs,T_a),T_a),
input ).
fof(cls_rev__filter_0_0,plain,
! [T_a,V_P,V_xs] :
( c_List_Orev(c_List_Ofilter(V_P,V_xs,T_a),T_a) = c_List_Ofilter(V_P,c_List_Orev(V_xs,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rev__filter_0]) ).
cnf(cls_append__eq__Cons__conv_4,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a),
input ).
fof(cls_append__eq__Cons__conv_4_0,plain,
! [T_a,V_x,V_xs] :
( c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__eq__Cons__conv_4]) ).
cnf(cls_substn__subst__0_0,axiom,
c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),
input ).
fof(cls_substn__subst__0_0_0,plain,
! [V_s,V_t] :
( c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat))
| $false ),
inference(orientation,[status(thm)],[cls_substn__subst__0_0]) ).
cnf(cls_liftn__0_0,axiom,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t,
input ).
fof(cls_liftn__0_0_0,plain,
! [V_k,V_t] :
( c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t
| $false ),
inference(orientation,[status(thm)],[cls_liftn__0_0]) ).
cnf(cls_dB_Orecs_I3_J_0,axiom,
c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a)),
input ).
fof(cls_dB_Orecs_I3_J_0_0,plain,
! [T_a,V_dB,V_f1,V_f2,V_f3] :
( c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_dB_Orecs_I3_J_0]) ).
cnf(cls_map__append_0,axiom,
c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a) = c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a),
input ).
fof(cls_map__append_0_0,plain,
! [T_a,T_b,V_f,V_xs,V_ys] :
( c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a) = c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_map__append_0]) ).
cnf(cls_beta_0,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat)))),
input ).
fof(cls_beta_0_0,plain,
! [V_s,V_t] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat))))
| $false ),
inference(orientation,[status(thm)],[cls_beta_0]) ).
cnf(cls_rev__rev__ident_0,axiom,
c_List_Orev(c_List_Orev(V_xs,T_a),T_a) = V_xs,
input ).
fof(cls_rev__rev__ident_0_0,plain,
! [T_a,V_xs] :
( c_List_Orev(c_List_Orev(V_xs,T_a),T_a) = V_xs
| $false ),
inference(orientation,[status(thm)],[cls_rev__rev__ident_0]) ).
cnf(cls_rev__swap_1,axiom,
c_List_Orev(c_List_Orev(V_ys,T_a),T_a) = V_ys,
input ).
fof(cls_rev__swap_1_0,plain,
! [T_a,V_ys] :
( c_List_Orev(c_List_Orev(V_ys,T_a),T_a) = V_ys
| $false ),
inference(orientation,[status(thm)],[cls_rev__swap_1]) ).
cnf(cls_rev__swap_0,axiom,
V_xs = c_List_Orev(c_List_Orev(V_xs,T_a),T_a),
input ).
fof(cls_rev__swap_0_0,plain,
! [T_a,V_xs] :
( c_List_Orev(c_List_Orev(V_xs,T_a),T_a) = V_xs
| $false ),
inference(orientation,[status(thm)],[cls_rev__swap_0]) ).
cnf(cls_rotate__map_0,axiom,
c_List_Orotate(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Orotate(V_n,V_xs,T_b),T_b,T_a),
input ).
fof(cls_rotate__map_0_0,plain,
! [T_a,T_b,V_f,V_n,V_xs] :
( c_List_Orotate(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Orotate(V_n,V_xs,T_b),T_b,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rotate__map_0]) ).
cnf(cls_Nitpick_Ortranclp__def_1,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)),
input ).
fof(cls_Nitpick_Ortranclp__def_1_0,plain,
! [T_a,V_r,V_x] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_Nitpick_Ortranclp__def_1]) ).
cnf(cls_rtranclp_Ortrancl__refl_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)),
input ).
fof(cls_rtranclp_Ortrancl__refl_0_0,plain,
! [T_a,V_a,V_r] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a))
| $false ),
inference(orientation,[status(thm)],[cls_rtranclp_Ortrancl__refl_0]) ).
cnf(cls_rev__map_0,axiom,
c_List_Orev(c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Orev(V_xs,T_b),T_b,T_a),
input ).
fof(cls_rev__map_0_0,plain,
! [T_a,T_b,V_f,V_xs] :
( c_List_Orev(c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Orev(V_xs,T_b),T_b,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rev__map_0]) ).
cnf(cls_dB_Osimps_I12_J_0,axiom,
c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(V_f3,V_dB),
input ).
fof(cls_dB_Osimps_I12_J_0_0,plain,
! [T_a,V_dB,V_f1,V_f2,V_f3] :
( c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(V_f3,V_dB)
| $false ),
inference(orientation,[status(thm)],[cls_dB_Osimps_I12_J_0]) ).
cnf(cls_substn__subst__n_0,axiom,
c_Lambda_Osubstn(V_t,V_s,V_n) = c_Lambda_Osubst(V_t,c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_n),
input ).
fof(cls_substn__subst__n_0_0,plain,
! [V_n,V_s,V_t] :
( c_Lambda_Osubstn(V_t,V_s,V_n) = c_Lambda_Osubst(V_t,c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_n)
| $false ),
inference(orientation,[status(thm)],[cls_substn__subst__n_0]) ).
cnf(cls_remdups__filter_0,axiom,
c_List_Oremdups(c_List_Ofilter(V_P,V_xs,T_a),T_a) = c_List_Ofilter(V_P,c_List_Oremdups(V_xs,T_a),T_a),
input ).
fof(cls_remdups__filter_0_0,plain,
! [T_a,V_P,V_xs] :
( c_List_Oremdups(c_List_Ofilter(V_P,V_xs,T_a),T_a) = c_List_Ofilter(V_P,c_List_Oremdups(V_xs,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_remdups__filter_0]) ).
cnf(cls_rev_Osimps_I2_J_0,axiom,
c_List_Orev(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Oappend(c_List_Orev(V_xs,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),
input ).
fof(cls_rev_Osimps_I2_J_0_0,plain,
! [T_a,V_x,V_xs] :
( c_List_Orev(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Oappend(c_List_Orev(V_xs,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rev_Osimps_I2_J_0]) ).
cnf(cls_rev__singleton__conv_1,axiom,
c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),
input ).
fof(cls_rev__singleton__conv_1_0,plain,
! [T_a,V_x] :
( c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rev__singleton__conv_1]) ).
cnf(cls_append__eq__Cons__conv_5,axiom,
c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a),
input ).
fof(cls_append__eq__Cons__conv_5_0,plain,
! [T_a,V_x,V_xa,V_zs] :
( c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__eq__Cons__conv_5]) ).
cnf(cls_append__Cons_0,axiom,
c_List_Oappend(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a),
input ).
fof(cls_append__Cons_0_0,plain,
! [T_a,V_x,V_xs,V_ys] :
( c_List_Oappend(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__Cons_0]) ).
cnf(cls_map__is__Nil__conv_1,axiom,
c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_map__is__Nil__conv_1_0,plain,
! [T_a,T_b,V_f] :
( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_map__is__Nil__conv_1]) ).
cnf(cls_listsp_ONil_0,axiom,
c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a),
input ).
fof(cls_listsp_ONil_0_0,plain,
! [T_a,V_A] :
( c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_listsp_ONil_0]) ).
cnf(cls_append__Nil2_0,axiom,
c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs,
input ).
fof(cls_append__Nil2_0_0,plain,
! [T_a,V_xs] :
( c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs
| $false ),
inference(orientation,[status(thm)],[cls_append__Nil2_0]) ).
cnf(cls_eq__Nil__appendI_0,axiom,
V_x = c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a),
input ).
fof(cls_eq__Nil__appendI_0_0,plain,
! [T_a,V_x] :
( c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a) = V_x
| $false ),
inference(orientation,[status(thm)],[cls_eq__Nil__appendI_0]) ).
cnf(cls_self__append__conv_1,axiom,
V_xs = c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),
input ).
fof(cls_self__append__conv_1_0,plain,
! [T_a,V_xs] :
( c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs
| $false ),
inference(orientation,[status(thm)],[cls_self__append__conv_1]) ).
cnf(cls_append__Nil_0,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys,
input ).
fof(cls_append__Nil_0_0,plain,
! [T_a,V_ys] :
( c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys
| $false ),
inference(orientation,[status(thm)],[cls_append__Nil_0]) ).
cnf(cls_self__append__conv2_1,axiom,
V_ys = c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a),
input ).
fof(cls_self__append__conv2_1_0,plain,
! [T_a,V_ys] :
( c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys
| $false ),
inference(orientation,[status(thm)],[cls_self__append__conv2_1]) ).
cnf(cls_remdups__eq__nil__iff_1,axiom,
c_List_Oremdups(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_remdups__eq__nil__iff_1_0,plain,
! [T_a] :
( c_List_Oremdups(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_remdups__eq__nil__iff_1]) ).
cnf(cls_not__Nil__step1_0,axiom,
~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a),
input ).
fof(cls_not__Nil__step1_0_0,plain,
! [T_a,V_r,V_xs] :
( ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_not__Nil__step1_0]) ).
cnf(cls_not__step1__Nil_0,axiom,
~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a),
input ).
fof(cls_not__step1__Nil_0_0,plain,
! [T_a,V_r,V_xs] :
( ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_not__step1__Nil_0]) ).
cnf(cls_list_Osimps_I2_J_0,axiom,
c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
input ).
fof(cls_list_Osimps_I2_J_0_0,plain,
! [T_a,V_a_H,V_list_H] :
( c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_list_Osimps_I2_J_0]) ).
cnf(cls_remdups__eq__nil__right__iff_1,axiom,
c_List_Olist_ONil(T_a) = c_List_Oremdups(c_List_Olist_ONil(T_a),T_a),
input ).
fof(cls_remdups__eq__nil__right__iff_1_0,plain,
! [T_a] :
( c_List_Olist_ONil(T_a) = c_List_Oremdups(c_List_Olist_ONil(T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_remdups__eq__nil__right__iff_1]) ).
cnf(cls_Nil__is__rev__conv_1,axiom,
c_List_Olist_ONil(T_a) = c_List_Orev(c_List_Olist_ONil(T_a),T_a),
input ).
fof(cls_Nil__is__rev__conv_1_0,plain,
! [T_a] :
( c_List_Olist_ONil(T_a) = c_List_Orev(c_List_Olist_ONil(T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Nil__is__rev__conv_1]) ).
cnf(cls_append__is__Nil__conv_2,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_append__is__Nil__conv_2_0,plain,
! [T_a] :
( c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__is__Nil__conv_2]) ).
cnf(cls_filter__append_0,axiom,
c_List_Ofilter(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Ofilter(V_P,V_xs,T_a),c_List_Ofilter(V_P,V_ys,T_a),T_a),
input ).
fof(cls_filter__append_0_0,plain,
! [T_a,V_P,V_xs,V_ys] :
( c_List_Ofilter(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Ofilter(V_P,V_xs,T_a),c_List_Ofilter(V_P,V_ys,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_filter__append_0]) ).
cnf(cls_rev__append_0,axiom,
c_List_Orev(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Orev(V_xs,T_a),T_a),
input ).
fof(cls_rev__append_0_0,plain,
! [T_a,V_xs,V_ys] :
( c_List_Orev(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Orev(V_xs,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rev__append_0]) ).
cnf(cls_rtranclp__idemp_0,axiom,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a),
input ).
fof(cls_rtranclp__idemp_0_0,plain,
! [T_a,V_r] :
( c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rtranclp__idemp_0]) ).
cnf(cls_singleton__rev__conv_1,axiom,
c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) = c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),
input ).
fof(cls_singleton__rev__conv_1_0,plain,
! [T_a,V_x] :
( c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) = c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_singleton__rev__conv_1]) ).
cnf(cls_map__update_0,axiom,
c_List_Omap(V_f,c_List_Olist__update(V_xs,V_k,V_y,T_b),T_b,T_a) = c_List_Olist__update(c_List_Omap(V_f,V_xs,T_b,T_a),V_k,hAPP(V_f,V_y),T_a),
input ).
fof(cls_map__update_0_0,plain,
! [T_a,T_b,V_f,V_k,V_xs,V_y] :
( c_List_Omap(V_f,c_List_Olist__update(V_xs,V_k,V_y,T_b),T_b,T_a) = c_List_Olist__update(c_List_Omap(V_f,V_xs,T_b,T_a),V_k,hAPP(V_f,V_y),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_map__update_0]) ).
cnf(cls_Cons__eq__append__conv_4,axiom,
c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a),
input ).
fof(cls_Cons__eq__append__conv_4_0,plain,
! [T_a,V_x,V_xs] :
( c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Cons__eq__append__conv_4]) ).
cnf(cls_list__update__code_I2_J_0,axiom,
c_List_Olist__update(c_List_Olist_OCons(V_x,V_xs,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) = c_List_Olist_OCons(V_y,V_xs,T_a),
input ).
fof(cls_list__update__code_I2_J_0_0,plain,
! [T_a,V_x,V_xs,V_y] :
( c_List_Olist__update(c_List_Olist_OCons(V_x,V_xs,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) = c_List_Olist_OCons(V_y,V_xs,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_list__update__code_I2_J_0]) ).
cnf(cls_not__Cons__self_0,axiom,
V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
input ).
fof(cls_not__Cons__self_0_0,plain,
! [T_a,V_x,V_xs] :
( V_xs != c_List_Olist_OCons(V_x,V_xs,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_not__Cons__self_0]) ).
cnf(cls_not__Cons__self2_0,axiom,
c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
input ).
fof(cls_not__Cons__self2_0_0,plain,
! [T_a,V_t,V_x] :
( c_List_Olist_OCons(V_x,V_t,T_a) != V_t
| $false ),
inference(orientation,[status(thm)],[cls_not__Cons__self2_0]) ).
cnf(cls_subst__lift_0,axiom,
c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t,
input ).
fof(cls_subst__lift_0_0,plain,
! [V_k,V_s,V_t] :
( c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t
| $false ),
inference(orientation,[status(thm)],[cls_subst__lift_0]) ).
cnf(cls_rev__eq__Cons__iff_1,axiom,
c_List_Orev(c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),T_a) = c_List_Olist_OCons(V_y,V_ys,T_a),
input ).
fof(cls_rev__eq__Cons__iff_1_0,plain,
! [T_a,V_y,V_ys] :
( c_List_Orev(c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),T_a) = c_List_Olist_OCons(V_y,V_ys,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rev__eq__Cons__iff_1]) ).
cnf(cls_Cons__eq__appendI_0,axiom,
c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a),
input ).
fof(cls_Cons__eq__appendI_0_0,plain,
! [T_a,V_x,V_xs1,V_zs] :
( c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Cons__eq__appendI_0]) ).
cnf(cls_Cons__eq__append__conv_5,axiom,
c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a),
input ).
fof(cls_Cons__eq__append__conv_5_0,plain,
! [T_a,V_x,V_xa,V_zs] :
( c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Cons__eq__append__conv_5]) ).
cnf(cls_remove1_Osimps_I2_J_0,axiom,
c_List_Oremove1(V_x,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = V_xs,
input ).
fof(cls_remove1_Osimps_I2_J_0_0,plain,
! [T_a,V_x,V_xs] :
( c_List_Oremove1(V_x,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = V_xs
| $false ),
inference(orientation,[status(thm)],[cls_remove1_Osimps_I2_J_0]) ).
cnf(cls_list_Osimps_I5_J_0,axiom,
c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_OCons(V_a,V_list,T_b),T_a,T_b) = hAPP(hAPP(V_f2,V_a),V_list),
input ).
fof(cls_list_Osimps_I5_J_0_0,plain,
! [T_a,T_b,V_a,V_f1,V_f2,V_list] :
( c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_OCons(V_a,V_list,T_b),T_a,T_b) = hAPP(hAPP(V_f2,V_a),V_list)
| $false ),
inference(orientation,[status(thm)],[cls_list_Osimps_I5_J_0]) ).
cnf(cls_map_Osimps_I2_J_0,axiom,
c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a),
input ).
fof(cls_map_Osimps_I2_J_0_0,plain,
! [T_a,T_b,V_f,V_x,V_xs] :
( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_map_Osimps_I2_J_0]) ).
cnf(cls_Cons__eq__map__conv_3,axiom,
c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a),
input ).
fof(cls_Cons__eq__map__conv_3_0,plain,
! [T_a,T_b,V_f,V_xa,V_xb] :
( c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Cons__eq__map__conv_3]) ).
cnf(cls_map__eq__Cons__conv_3,axiom,
c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a),
input ).
fof(cls_map__eq__Cons__conv_3_0,plain,
! [T_a,T_b,V_f,V_x,V_xa] :
( c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_map__eq__Cons__conv_3]) ).
cnf(cls_list__update__length_0,axiom,
c_List_Olist__update(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,V_ys,T_a),T_a),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_y,T_a) = c_List_Oappend(V_xs,c_List_Olist_OCons(V_y,V_ys,T_a),T_a),
input ).
fof(cls_list__update__length_0_0,plain,
! [T_a,V_x,V_xs,V_y,V_ys] :
( c_List_Olist__update(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,V_ys,T_a),T_a),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_y,T_a) = c_List_Oappend(V_xs,c_List_Olist_OCons(V_y,V_ys,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_list__update__length_0]) ).
cnf(cls_replicate__append__same_0,axiom,
c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a),
input ).
fof(cls_replicate__append__same_0_0,plain,
! [T_a,V_i,V_x] :
( c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_replicate__append__same_0]) ).
cnf(cls_replicate__app__Cons__same_0,axiom,
c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a),
input ).
fof(cls_replicate__app__Cons__same_0_0,plain,
! [T_a,V_n,V_x,V_xs] :
( c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_replicate__app__Cons__same_0]) ).
cnf(cls_empty__replicate_1,axiom,
c_List_Olist_ONil(T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a),
input ).
fof(cls_empty__replicate_1_0,plain,
! [T_a,V_x] :
( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_empty__replicate_1]) ).
cnf(cls_length__0__conv_1,axiom,
c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat),
input ).
fof(cls_length__0__conv_1_0,plain,
! [T_a] :
( c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_length__0__conv_1]) ).
cnf(cls_replicate__empty_1,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a),
input ).
fof(cls_replicate__empty_1_0,plain,
! [T_a,V_x] :
( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_replicate__empty_1]) ).
cnf(cls_length__rev_0,axiom,
c_Nat_Osize__class_Osize(c_List_Orev(V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),
input ).
fof(cls_length__rev_0_0,plain,
! [T_a,V_xs] :
( c_Nat_Osize__class_Osize(c_List_Orev(V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))
| $false ),
inference(orientation,[status(thm)],[cls_length__rev_0]) ).
cnf(cls_conversep__conversep_0,axiom,
c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r,
input ).
fof(cls_conversep__conversep_0_0,plain,
! [T_a,T_b,V_r] :
( c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r
| $false ),
inference(orientation,[status(thm)],[cls_conversep__conversep_0]) ).
cnf(cls_foldr_Osimps_I2_J_0,axiom,
c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)),
input ).
fof(cls_foldr_Osimps_I2_J_0_0,plain,
! [T_a,T_b,V_a,V_f,V_x,V_xs] :
( c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_foldr_Osimps_I2_J_0]) ).
cnf(cls_length__replicate_0,axiom,
c_Nat_Osize__class_Osize(c_List_Oreplicate(V_n,V_x,T_a),tc_List_Olist(T_a)) = V_n,
input ).
fof(cls_length__replicate_0_0,plain,
! [T_a,V_n,V_x] :
( c_Nat_Osize__class_Osize(c_List_Oreplicate(V_n,V_x,T_a),tc_List_Olist(T_a)) = V_n
| $false ),
inference(orientation,[status(thm)],[cls_length__replicate_0]) ).
cnf(cls_neq0__conv_1,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
input ).
fof(cls_neq0__conv_1_0,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_neq0__conv_1]) ).
cnf(cls_append__replicate__commute_0,axiom,
c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oappend(c_List_Oreplicate(V_k,V_x,T_a),c_List_Oreplicate(V_n,V_x,T_a),T_a),
input ).
fof(cls_append__replicate__commute_0_0,plain,
! [T_a,V_k,V_n,V_x] :
( c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oappend(c_List_Oreplicate(V_k,V_x,T_a),c_List_Oreplicate(V_n,V_x,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_append__replicate__commute_0]) ).
cnf(cls_less__not__refl_0,axiom,
~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
input ).
fof(cls_less__not__refl_0_0,plain,
! [V_n] :
( ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_less__not__refl_0]) ).
cnf(cls_nat__less__le_1,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
input ).
fof(cls_nat__less__le_1_0,plain,
! [V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_nat__less__le_1]) ).
cnf(cls_length__rotate_0,axiom,
c_Nat_Osize__class_Osize(c_List_Orotate(V_n,V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),
input ).
fof(cls_length__rotate_0_0,plain,
! [T_a,V_n,V_xs] :
( c_Nat_Osize__class_Osize(c_List_Orotate(V_n,V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))
| $false ),
inference(orientation,[status(thm)],[cls_length__rotate_0]) ).
cnf(cls_conversep__eq_0,axiom,
c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a),
input ).
fof(cls_conversep__eq_0_0,plain,
! [T_a] :
( c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_conversep__eq_0]) ).
cnf(cls_foldr__append_0,axiom,
c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a) = c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a),
input ).
fof(cls_foldr__append_0_0,plain,
! [T_a,T_b,V_a,V_f,V_xs,V_ys] :
( c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a) = c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_foldr__append_0]) ).
cnf(cls_rev__replicate_0,axiom,
c_List_Orev(c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_List_Oreplicate(V_n,V_x,T_a),
input ).
fof(cls_rev__replicate_0_0,plain,
! [T_a,V_n,V_x] :
( c_List_Orev(c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_List_Oreplicate(V_n,V_x,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rev__replicate_0]) ).
cnf(cls_map__replicate_0,axiom,
c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a) = c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a),
input ).
fof(cls_map__replicate_0_0,plain,
! [T_a,T_b,V_f,V_n,V_x] :
( c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a) = c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_map__replicate_0]) ).
cnf(cls_length__map_0,axiom,
c_Nat_Osize__class_Osize(c_List_Omap(V_f,V_xs,T_b,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_b)),
input ).
fof(cls_length__map_0_0,plain,
! [T_a,T_b,V_f,V_xs] :
( c_Nat_Osize__class_Osize(c_List_Omap(V_f,V_xs,T_b,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_b))
| $false ),
inference(orientation,[status(thm)],[cls_length__map_0]) ).
cnf(cls_gr__implies__not0_0,axiom,
~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
input ).
fof(cls_gr__implies__not0_0_0,plain,
! [V_m] :
( ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_gr__implies__not0_0]) ).
cnf(cls_not__less0_0,axiom,
~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
input ).
fof(cls_not__less0_0_0,plain,
! [V_n] :
( ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_not__less0_0]) ).
cnf(cls_replicate__eq__replicate_2,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a),
input ).
fof(cls_replicate__eq__replicate_2_0,plain,
! [T_a,V_x,V_y] :
( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a)
| c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) ),
inference(orientation,[status(thm)],[cls_replicate__eq__replicate_2]) ).
cnf(cls_length__list__update_0,axiom,
c_Nat_Osize__class_Osize(c_List_Olist__update(V_xs,V_i,V_x,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),
input ).
fof(cls_length__list__update_0_0,plain,
! [T_a,V_i,V_x,V_xs] :
( c_Nat_Osize__class_Osize(c_List_Olist__update(V_xs,V_i,V_x,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a))
| $false ),
inference(orientation,[status(thm)],[cls_length__list__update_0]) ).
cnf(cls_length__greater__0__conv_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)),tc_nat),
input ).
fof(cls_length__greater__0__conv_0_0,plain,
! [T_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)),tc_nat)
| $false ),
inference(orientation,[status(thm)],[cls_length__greater__0__conv_0]) ).
cnf(cls_foldr_Osimps_I1_J_0,axiom,
c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a,
input ).
fof(cls_foldr_Osimps_I1_J_0_0,plain,
! [T_a,T_b,V_a,V_f] :
( c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a
| $false ),
inference(orientation,[status(thm)],[cls_foldr_Osimps_I1_J_0]) ).
fof(def_lhs_atom1,axiom,
! [V_f,V_a,T_b,T_a] :
( lhs_atom1(V_f,V_a,T_b,T_a)
<=> c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a ),
inference(definition,[],[]) ).
fof(to_be_clausified_0,plain,
! [T_a,T_b,V_a,V_f] :
( lhs_atom1(V_f,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_foldr_Osimps_I1_J_0_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [T_a] :
( lhs_atom2(T_a)
<=> ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)),tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_1,plain,
! [T_a] :
( lhs_atom2(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_length__greater__0__conv_0_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [V_xs,V_x,V_i,T_a] :
( lhs_atom3(V_xs,V_x,V_i,T_a)
<=> c_Nat_Osize__class_Osize(c_List_Olist__update(V_xs,V_i,V_x,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_2,plain,
! [T_a,V_i,V_x,V_xs] :
( lhs_atom3(V_xs,V_x,V_i,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_length__list__update_0_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [V_y,V_x,T_a] :
( lhs_atom4(V_y,V_x,T_a)
<=> c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_3,plain,
! [T_a,V_x,V_y] :
( lhs_atom4(V_y,V_x,T_a)
| c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) ),
inference(fold_definition,[status(thm)],[cls_replicate__eq__replicate_2_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [V_n] :
( lhs_atom5(V_n)
<=> ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_4,plain,
! [V_n] :
( lhs_atom5(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__less0_0_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [V_m] :
( lhs_atom6(V_m)
<=> ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_5,plain,
! [V_m] :
( lhs_atom6(V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_gr__implies__not0_0_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [V_xs,V_f,T_b,T_a] :
( lhs_atom7(V_xs,V_f,T_b,T_a)
<=> c_Nat_Osize__class_Osize(c_List_Omap(V_f,V_xs,T_b,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_b)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_6,plain,
! [T_a,T_b,V_f,V_xs] :
( lhs_atom7(V_xs,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_length__map_0_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [V_x,V_n,V_f,T_b,T_a] :
( lhs_atom8(V_x,V_n,V_f,T_b,T_a)
<=> c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a) = c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_7,plain,
! [T_a,T_b,V_f,V_n,V_x] :
( lhs_atom8(V_x,V_n,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__replicate_0_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [V_x,V_n,T_a] :
( lhs_atom9(V_x,V_n,T_a)
<=> c_List_Orev(c_List_Oreplicate(V_n,V_x,T_a),T_a) = c_List_Oreplicate(V_n,V_x,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_8,plain,
! [T_a,V_n,V_x] :
( lhs_atom9(V_x,V_n,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rev__replicate_0_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [V_ys,V_xs,V_f,V_a,T_b,T_a] :
( lhs_atom10(V_ys,V_xs,V_f,V_a,T_b,T_a)
<=> c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a) = c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_9,plain,
! [T_a,T_b,V_a,V_f,V_xs,V_ys] :
( lhs_atom10(V_ys,V_xs,V_f,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_foldr__append_0_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [T_a] :
( lhs_atom11(T_a)
<=> c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_10,plain,
! [T_a] :
( lhs_atom11(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_conversep__eq_0_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [V_xs,V_n,T_a] :
( lhs_atom12(V_xs,V_n,T_a)
<=> c_Nat_Osize__class_Osize(c_List_Orotate(V_n,V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_11,plain,
! [T_a,V_n,V_xs] :
( lhs_atom12(V_xs,V_n,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_length__rotate_0_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [V_x] :
( lhs_atom13(V_x)
<=> ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_12,plain,
! [V_x] :
( lhs_atom13(V_x)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__less__le_1_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [V_n] :
( lhs_atom14(V_n)
<=> ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_13,plain,
! [V_n] :
( lhs_atom14(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_less__not__refl_0_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [V_x,V_n,V_k,T_a] :
( lhs_atom15(V_x,V_n,V_k,T_a)
<=> c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oappend(c_List_Oreplicate(V_k,V_x,T_a),c_List_Oreplicate(V_n,V_x,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_14,plain,
! [T_a,V_k,V_n,V_x] :
( lhs_atom15(V_x,V_n,V_k,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__replicate__commute_0_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
( lhs_atom16
<=> ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_15,plain,
( lhs_atom16
| $false ),
inference(fold_definition,[status(thm)],[cls_neq0__conv_1_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [V_x,V_n,T_a] :
( lhs_atom17(V_x,V_n,T_a)
<=> c_Nat_Osize__class_Osize(c_List_Oreplicate(V_n,V_x,T_a),tc_List_Olist(T_a)) = V_n ),
inference(definition,[],[]) ).
fof(to_be_clausified_16,plain,
! [T_a,V_n,V_x] :
( lhs_atom17(V_x,V_n,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_length__replicate_0_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
! [V_xs,V_x,V_f,V_a,T_b,T_a] :
( lhs_atom18(V_xs,V_x,V_f,V_a,T_b,T_a)
<=> c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_17,plain,
! [T_a,T_b,V_a,V_f,V_x,V_xs] :
( lhs_atom18(V_xs,V_x,V_f,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_foldr_Osimps_I2_J_0_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [V_r,T_b,T_a] :
( lhs_atom19(V_r,T_b,T_a)
<=> c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r ),
inference(definition,[],[]) ).
fof(to_be_clausified_18,plain,
! [T_a,T_b,V_r] :
( lhs_atom19(V_r,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_conversep__conversep_0_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [V_xs,T_a] :
( lhs_atom20(V_xs,T_a)
<=> c_Nat_Osize__class_Osize(c_List_Orev(V_xs,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_19,plain,
! [T_a,V_xs] :
( lhs_atom20(V_xs,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_length__rev_0_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [V_x,T_a] :
( lhs_atom21(V_x,T_a)
<=> c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_20,plain,
! [T_a,V_x] :
( lhs_atom21(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_replicate__empty_1_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [T_a] :
( lhs_atom22(T_a)
<=> c_Nat_Osize__class_Osize(c_List_Olist_ONil(T_a),tc_List_Olist(T_a)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_21,plain,
! [T_a] :
( lhs_atom22(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_length__0__conv_1_0,def_lhs_atom22]) ).
fof(to_be_clausified_22,plain,
! [T_a,V_x] :
( lhs_atom21(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__replicate_1_0,def_lhs_atom21]) ).
fof(def_lhs_atom23,axiom,
! [V_xs,V_x,V_n,T_a] :
( lhs_atom23(V_xs,V_x,V_n,T_a)
<=> c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_23,plain,
! [T_a,V_n,V_x,V_xs] :
( lhs_atom23(V_xs,V_x,V_n,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_replicate__app__Cons__same_0_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [V_x,V_i,T_a] :
( lhs_atom24(V_x,V_i,T_a)
<=> c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_24,plain,
! [T_a,V_i,V_x] :
( lhs_atom24(V_x,V_i,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_replicate__append__same_0_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [V_ys,V_y,V_xs,V_x,T_a] :
( lhs_atom25(V_ys,V_y,V_xs,V_x,T_a)
<=> c_List_Olist__update(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,V_ys,T_a),T_a),c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),V_y,T_a) = c_List_Oappend(V_xs,c_List_Olist_OCons(V_y,V_ys,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_25,plain,
! [T_a,V_x,V_xs,V_y,V_ys] :
( lhs_atom25(V_ys,V_y,V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_list__update__length_0_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [V_xa,V_x,V_f,T_b,T_a] :
( lhs_atom26(V_xa,V_x,V_f,T_b,T_a)
<=> c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_26,plain,
! [T_a,T_b,V_f,V_x,V_xa] :
( lhs_atom26(V_xa,V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__eq__Cons__conv_3_0,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [V_xb,V_xa,V_f,T_b,T_a] :
( lhs_atom27(V_xb,V_xa,V_f,T_b,T_a)
<=> c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_27,plain,
! [T_a,T_b,V_f,V_xa,V_xb] :
( lhs_atom27(V_xb,V_xa,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Cons__eq__map__conv_3_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [V_xs,V_x,V_f,T_b,T_a] :
( lhs_atom28(V_xs,V_x,V_f,T_b,T_a)
<=> c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_28,plain,
! [T_a,T_b,V_f,V_x,V_xs] :
( lhs_atom28(V_xs,V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map_Osimps_I2_J_0_0,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [V_list,V_f2,V_f1,V_a,T_b,T_a] :
( lhs_atom29(V_list,V_f2,V_f1,V_a,T_b,T_a)
<=> c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_OCons(V_a,V_list,T_b),T_a,T_b) = hAPP(hAPP(V_f2,V_a),V_list) ),
inference(definition,[],[]) ).
fof(to_be_clausified_29,plain,
! [T_a,T_b,V_a,V_f1,V_f2,V_list] :
( lhs_atom29(V_list,V_f2,V_f1,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_list_Osimps_I5_J_0_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [V_xs,V_x,T_a] :
( lhs_atom30(V_xs,V_x,T_a)
<=> c_List_Oremove1(V_x,c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = V_xs ),
inference(definition,[],[]) ).
fof(to_be_clausified_30,plain,
! [T_a,V_x,V_xs] :
( lhs_atom30(V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_remove1_Osimps_I2_J_0_0,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
! [V_zs,V_xa,V_x,T_a] :
( lhs_atom31(V_zs,V_xa,V_x,T_a)
<=> c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_31,plain,
! [T_a,V_x,V_xa,V_zs] :
( lhs_atom31(V_zs,V_xa,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Cons__eq__append__conv_5_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
! [V_zs,V_xs1,V_x,T_a] :
( lhs_atom32(V_zs,V_xs1,V_x,T_a)
<=> c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_32,plain,
! [T_a,V_x,V_xs1,V_zs] :
( lhs_atom32(V_zs,V_xs1,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Cons__eq__appendI_0_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
! [V_ys,V_y,T_a] :
( lhs_atom33(V_ys,V_y,T_a)
<=> c_List_Orev(c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),T_a) = c_List_Olist_OCons(V_y,V_ys,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_33,plain,
! [T_a,V_y,V_ys] :
( lhs_atom33(V_ys,V_y,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rev__eq__Cons__iff_1_0,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [V_t,V_s,V_k] :
( lhs_atom34(V_t,V_s,V_k)
<=> c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ),
inference(definition,[],[]) ).
fof(to_be_clausified_34,plain,
! [V_k,V_s,V_t] :
( lhs_atom34(V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__lift_0_0,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [V_x,V_t,T_a] :
( lhs_atom35(V_x,V_t,T_a)
<=> c_List_Olist_OCons(V_x,V_t,T_a) != V_t ),
inference(definition,[],[]) ).
fof(to_be_clausified_35,plain,
! [T_a,V_t,V_x] :
( lhs_atom35(V_x,V_t,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__Cons__self2_0_0,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
! [V_xs,V_x,T_a] :
( lhs_atom36(V_xs,V_x,T_a)
<=> V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_36,plain,
! [T_a,V_x,V_xs] :
( lhs_atom36(V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__Cons__self_0_0,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
! [V_y,V_xs,V_x,T_a] :
( lhs_atom37(V_y,V_xs,V_x,T_a)
<=> c_List_Olist__update(c_List_Olist_OCons(V_x,V_xs,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) = c_List_Olist_OCons(V_y,V_xs,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_37,plain,
! [T_a,V_x,V_xs,V_y] :
( lhs_atom37(V_y,V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_list__update__code_I2_J_0_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
! [V_xs,V_x,T_a] :
( lhs_atom38(V_xs,V_x,T_a)
<=> c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_38,plain,
! [T_a,V_x,V_xs] :
( lhs_atom38(V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Cons__eq__append__conv_4_0,def_lhs_atom38]) ).
fof(def_lhs_atom39,axiom,
! [V_y,V_xs,V_k,V_f,T_b,T_a] :
( lhs_atom39(V_y,V_xs,V_k,V_f,T_b,T_a)
<=> c_List_Omap(V_f,c_List_Olist__update(V_xs,V_k,V_y,T_b),T_b,T_a) = c_List_Olist__update(c_List_Omap(V_f,V_xs,T_b,T_a),V_k,hAPP(V_f,V_y),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_39,plain,
! [T_a,T_b,V_f,V_k,V_xs,V_y] :
( lhs_atom39(V_y,V_xs,V_k,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__update_0_0,def_lhs_atom39]) ).
fof(def_lhs_atom40,axiom,
! [V_x,T_a] :
( lhs_atom40(V_x,T_a)
<=> c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) = c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_40,plain,
! [T_a,V_x] :
( lhs_atom40(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_singleton__rev__conv_1_0,def_lhs_atom40]) ).
fof(def_lhs_atom41,axiom,
! [V_r,T_a] :
( lhs_atom41(V_r,T_a)
<=> c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_41,plain,
! [T_a,V_r] :
( lhs_atom41(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtranclp__idemp_0_0,def_lhs_atom41]) ).
fof(def_lhs_atom42,axiom,
! [V_ys,V_xs,T_a] :
( lhs_atom42(V_ys,V_xs,T_a)
<=> c_List_Orev(c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Orev(V_xs,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_42,plain,
! [T_a,V_xs,V_ys] :
( lhs_atom42(V_ys,V_xs,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rev__append_0_0,def_lhs_atom42]) ).
fof(def_lhs_atom43,axiom,
! [V_ys,V_xs,V_P,T_a] :
( lhs_atom43(V_ys,V_xs,V_P,T_a)
<=> c_List_Ofilter(V_P,c_List_Oappend(V_xs,V_ys,T_a),T_a) = c_List_Oappend(c_List_Ofilter(V_P,V_xs,T_a),c_List_Ofilter(V_P,V_ys,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_43,plain,
! [T_a,V_P,V_xs,V_ys] :
( lhs_atom43(V_ys,V_xs,V_P,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_filter__append_0_0,def_lhs_atom43]) ).
fof(def_lhs_atom44,axiom,
! [T_a] :
( lhs_atom44(T_a)
<=> c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_44,plain,
! [T_a] :
( lhs_atom44(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__is__Nil__conv_2_0,def_lhs_atom44]) ).
fof(def_lhs_atom45,axiom,
! [T_a] :
( lhs_atom45(T_a)
<=> c_List_Olist_ONil(T_a) = c_List_Orev(c_List_Olist_ONil(T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_45,plain,
! [T_a] :
( lhs_atom45(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nil__is__rev__conv_1_0,def_lhs_atom45]) ).
fof(def_lhs_atom46,axiom,
! [T_a] :
( lhs_atom46(T_a)
<=> c_List_Olist_ONil(T_a) = c_List_Oremdups(c_List_Olist_ONil(T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_46,plain,
! [T_a] :
( lhs_atom46(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_remdups__eq__nil__right__iff_1_0,def_lhs_atom46]) ).
fof(def_lhs_atom47,axiom,
! [V_list_H,V_a_H,T_a] :
( lhs_atom47(V_list_H,V_a_H,T_a)
<=> c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_47,plain,
! [T_a,V_a_H,V_list_H] :
( lhs_atom47(V_list_H,V_a_H,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_list_Osimps_I2_J_0_0,def_lhs_atom47]) ).
fof(def_lhs_atom48,axiom,
! [V_xs,V_r,T_a] :
( lhs_atom48(V_xs,V_r,T_a)
<=> ~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_48,plain,
! [T_a,V_r,V_xs] :
( lhs_atom48(V_xs,V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__step1__Nil_0_0,def_lhs_atom48]) ).
fof(def_lhs_atom49,axiom,
! [V_xs,V_r,T_a] :
( lhs_atom49(V_xs,V_r,T_a)
<=> ~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_49,plain,
! [T_a,V_r,V_xs] :
( lhs_atom49(V_xs,V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__Nil__step1_0_0,def_lhs_atom49]) ).
fof(def_lhs_atom50,axiom,
! [T_a] :
( lhs_atom50(T_a)
<=> c_List_Oremdups(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_50,plain,
! [T_a] :
( lhs_atom50(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_remdups__eq__nil__iff_1_0,def_lhs_atom50]) ).
fof(def_lhs_atom51,axiom,
! [V_ys,T_a] :
( lhs_atom51(V_ys,T_a)
<=> c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys ),
inference(definition,[],[]) ).
fof(to_be_clausified_51,plain,
! [T_a,V_ys] :
( lhs_atom51(V_ys,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_self__append__conv2_1_0,def_lhs_atom51]) ).
fof(to_be_clausified_52,plain,
! [T_a,V_ys] :
( lhs_atom51(V_ys,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__Nil_0_0,def_lhs_atom51]) ).
fof(def_lhs_atom52,axiom,
! [V_xs,T_a] :
( lhs_atom52(V_xs,T_a)
<=> c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs ),
inference(definition,[],[]) ).
fof(to_be_clausified_53,plain,
! [T_a,V_xs] :
( lhs_atom52(V_xs,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_self__append__conv_1_0,def_lhs_atom52]) ).
fof(def_lhs_atom53,axiom,
! [V_x,T_a] :
( lhs_atom53(V_x,T_a)
<=> c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a) = V_x ),
inference(definition,[],[]) ).
fof(to_be_clausified_54,plain,
! [T_a,V_x] :
( lhs_atom53(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_eq__Nil__appendI_0_0,def_lhs_atom53]) ).
fof(to_be_clausified_55,plain,
! [T_a,V_xs] :
( lhs_atom52(V_xs,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__Nil2_0_0,def_lhs_atom52]) ).
fof(def_lhs_atom54,axiom,
! [V_A,T_a] :
( lhs_atom54(V_A,T_a)
<=> c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_56,plain,
! [T_a,V_A] :
( lhs_atom54(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_listsp_ONil_0_0,def_lhs_atom54]) ).
fof(def_lhs_atom55,axiom,
! [V_f,T_b,T_a] :
( lhs_atom55(V_f,T_b,T_a)
<=> c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_57,plain,
! [T_a,T_b,V_f] :
( lhs_atom55(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__is__Nil__conv_1_0,def_lhs_atom55]) ).
fof(def_lhs_atom56,axiom,
! [V_ys,V_xs,V_x,T_a] :
( lhs_atom56(V_ys,V_xs,V_x,T_a)
<=> c_List_Oappend(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_58,plain,
! [T_a,V_x,V_xs,V_ys] :
( lhs_atom56(V_ys,V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__Cons_0_0,def_lhs_atom56]) ).
fof(def_lhs_atom57,axiom,
! [V_zs,V_xa,V_x,T_a] :
( lhs_atom57(V_zs,V_xa,V_x,T_a)
<=> c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_59,plain,
! [T_a,V_x,V_xa,V_zs] :
( lhs_atom57(V_zs,V_xa,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__Cons__conv_5_0,def_lhs_atom57]) ).
fof(def_lhs_atom58,axiom,
! [V_x,T_a] :
( lhs_atom58(V_x,T_a)
<=> c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_60,plain,
! [T_a,V_x] :
( lhs_atom58(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rev__singleton__conv_1_0,def_lhs_atom58]) ).
fof(def_lhs_atom59,axiom,
! [V_xs,V_x,T_a] :
( lhs_atom59(V_xs,V_x,T_a)
<=> c_List_Orev(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Oappend(c_List_Orev(V_xs,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_61,plain,
! [T_a,V_x,V_xs] :
( lhs_atom59(V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rev_Osimps_I2_J_0_0,def_lhs_atom59]) ).
fof(def_lhs_atom60,axiom,
! [V_xs,V_P,T_a] :
( lhs_atom60(V_xs,V_P,T_a)
<=> c_List_Oremdups(c_List_Ofilter(V_P,V_xs,T_a),T_a) = c_List_Ofilter(V_P,c_List_Oremdups(V_xs,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_62,plain,
! [T_a,V_P,V_xs] :
( lhs_atom60(V_xs,V_P,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_remdups__filter_0_0,def_lhs_atom60]) ).
fof(def_lhs_atom61,axiom,
! [V_t,V_s,V_n] :
( lhs_atom61(V_t,V_s,V_n)
<=> c_Lambda_Osubstn(V_t,V_s,V_n) = c_Lambda_Osubst(V_t,c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_n) ),
inference(definition,[],[]) ).
fof(to_be_clausified_63,plain,
! [V_n,V_s,V_t] :
( lhs_atom61(V_t,V_s,V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_substn__subst__n_0_0,def_lhs_atom61]) ).
fof(def_lhs_atom62,axiom,
! [V_f3,V_f2,V_f1,V_dB,T_a] :
( lhs_atom62(V_f3,V_f2,V_f1,V_dB,T_a)
<=> c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(V_f3,V_dB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_64,plain,
! [T_a,V_dB,V_f1,V_f2,V_f3] :
( lhs_atom62(V_f3,V_f2,V_f1,V_dB,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I12_J_0_0,def_lhs_atom62]) ).
fof(def_lhs_atom63,axiom,
! [V_xs,V_f,T_b,T_a] :
( lhs_atom63(V_xs,V_f,T_b,T_a)
<=> c_List_Orev(c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Orev(V_xs,T_b),T_b,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_65,plain,
! [T_a,T_b,V_f,V_xs] :
( lhs_atom63(V_xs,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rev__map_0_0,def_lhs_atom63]) ).
fof(def_lhs_atom64,axiom,
! [V_r,V_a,T_a] :
( lhs_atom64(V_r,V_a,T_a)
<=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_66,plain,
! [T_a,V_a,V_r] :
( lhs_atom64(V_r,V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtranclp_Ortrancl__refl_0_0,def_lhs_atom64]) ).
fof(def_lhs_atom65,axiom,
! [V_x,V_r,T_a] :
( lhs_atom65(V_x,V_r,T_a)
<=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_67,plain,
! [T_a,V_r,V_x] :
( lhs_atom65(V_x,V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nitpick_Ortranclp__def_1_0,def_lhs_atom65]) ).
fof(def_lhs_atom66,axiom,
! [V_xs,V_n,V_f,T_b,T_a] :
( lhs_atom66(V_xs,V_n,V_f,T_b,T_a)
<=> c_List_Orotate(V_n,c_List_Omap(V_f,V_xs,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Orotate(V_n,V_xs,T_b),T_b,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_68,plain,
! [T_a,T_b,V_f,V_n,V_xs] :
( lhs_atom66(V_xs,V_n,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rotate__map_0_0,def_lhs_atom66]) ).
fof(def_lhs_atom67,axiom,
! [V_xs,T_a] :
( lhs_atom67(V_xs,T_a)
<=> c_List_Orev(c_List_Orev(V_xs,T_a),T_a) = V_xs ),
inference(definition,[],[]) ).
fof(to_be_clausified_69,plain,
! [T_a,V_xs] :
( lhs_atom67(V_xs,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rev__swap_0_0,def_lhs_atom67]) ).
fof(def_lhs_atom68,axiom,
! [V_ys,T_a] :
( lhs_atom68(V_ys,T_a)
<=> c_List_Orev(c_List_Orev(V_ys,T_a),T_a) = V_ys ),
inference(definition,[],[]) ).
fof(to_be_clausified_70,plain,
! [T_a,V_ys] :
( lhs_atom68(V_ys,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rev__swap_1_0,def_lhs_atom68]) ).
fof(to_be_clausified_71,plain,
! [T_a,V_xs] :
( lhs_atom67(V_xs,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rev__rev__ident_0_0,def_lhs_atom67]) ).
fof(def_lhs_atom69,axiom,
! [V_t,V_s] :
( lhs_atom69(V_t,V_s)
<=> hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat)))) ),
inference(definition,[],[]) ).
fof(to_be_clausified_72,plain,
! [V_s,V_t] :
( lhs_atom69(V_t,V_s)
| $false ),
inference(fold_definition,[status(thm)],[cls_beta_0_0,def_lhs_atom69]) ).
fof(def_lhs_atom70,axiom,
! [V_ys,V_xs,V_f,T_b,T_a] :
( lhs_atom70(V_ys,V_xs,V_f,T_b,T_a)
<=> c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a) = c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_73,plain,
! [T_a,T_b,V_f,V_xs,V_ys] :
( lhs_atom70(V_ys,V_xs,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__append_0_0,def_lhs_atom70]) ).
fof(def_lhs_atom71,axiom,
! [V_f3,V_f2,V_f1,V_dB,T_a] :
( lhs_atom71(V_f3,V_f2,V_f1,V_dB,T_a)
<=> c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_74,plain,
! [T_a,V_dB,V_f1,V_f2,V_f3] :
( lhs_atom71(V_f3,V_f2,V_f1,V_dB,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Orecs_I3_J_0_0,def_lhs_atom71]) ).
fof(def_lhs_atom72,axiom,
! [V_t,V_k] :
( lhs_atom72(V_t,V_k)
<=> c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t ),
inference(definition,[],[]) ).
fof(to_be_clausified_75,plain,
! [V_k,V_t] :
( lhs_atom72(V_t,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_liftn__0_0_0,def_lhs_atom72]) ).
fof(def_lhs_atom73,axiom,
! [V_t,V_s] :
( lhs_atom73(V_t,V_s)
<=> c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_76,plain,
! [V_s,V_t] :
( lhs_atom73(V_t,V_s)
| $false ),
inference(fold_definition,[status(thm)],[cls_substn__subst__0_0_0,def_lhs_atom73]) ).
fof(def_lhs_atom74,axiom,
! [V_xs,V_x,T_a] :
( lhs_atom74(V_xs,V_x,T_a)
<=> c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_77,plain,
! [T_a,V_x,V_xs] :
( lhs_atom74(V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__Cons__conv_4_0,def_lhs_atom74]) ).
fof(def_lhs_atom75,axiom,
! [V_xs,V_P,T_a] :
( lhs_atom75(V_xs,V_P,T_a)
<=> c_List_Orev(c_List_Ofilter(V_P,V_xs,T_a),T_a) = c_List_Ofilter(V_P,c_List_Orev(V_xs,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_78,plain,
! [T_a,V_P,V_xs] :
( lhs_atom75(V_xs,V_P,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rev__filter_0_0,def_lhs_atom75]) ).
fof(def_lhs_atom76,axiom,
! [V_y,V_xs,V_x,V_i,T_a] :
( lhs_atom76(V_y,V_xs,V_x,V_i,T_a)
<=> c_List_Olist__update(c_List_Olist__update(V_xs,V_i,V_x,T_a),V_i,V_y,T_a) = c_List_Olist__update(V_xs,V_i,V_y,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_79,plain,
! [T_a,V_i,V_x,V_xs,V_y] :
( lhs_atom76(V_y,V_xs,V_x,V_i,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_list__update__overwrite_0_0,def_lhs_atom76]) ).
fof(def_lhs_atom77,axiom,
! [V_zs,V_ys,V_xs,T_a] :
( lhs_atom77(V_zs,V_ys,V_xs,T_a)
<=> c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a) = c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_80,plain,
! [T_a,V_xs,V_ys,V_zs] :
( lhs_atom77(V_zs,V_ys,V_xs,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__assoc_0_0,def_lhs_atom77]) ).
fof(def_lhs_atom78,axiom,
! [V_xs1,V_xs,V_us,T_a] :
( lhs_atom78(V_xs1,V_xs,V_us,T_a)
<=> c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_81,plain,
! [T_a,V_us,V_xs,V_xs1] :
( lhs_atom78(V_xs1,V_xs,V_us,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__appendI_0_0,def_lhs_atom78]) ).
fof(def_lhs_atom79,axiom,
! [V_zs,V_ys,V_x,T_a] :
( lhs_atom79(V_zs,V_ys,V_x,T_a)
<=> c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a) = c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_82,plain,
! [T_a,V_x,V_ys,V_zs] :
( lhs_atom79(V_zs,V_ys,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__append__conv2_4_0,def_lhs_atom79]) ).
fof(def_lhs_atom80,axiom,
! [V_xs,V_x,V_ts,T_a] :
( lhs_atom80(V_xs,V_x,V_ts,T_a)
<=> c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_83,plain,
! [T_a,V_ts,V_x,V_xs] :
( lhs_atom80(V_xs,V_x,V_ts,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__append__conv2_5_0,def_lhs_atom80]) ).
fof(def_lhs_atom81,axiom,
! [V_f,T_b,T_a] :
( lhs_atom81(V_f,T_b,T_a)
<=> c_List_Ofiltermap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_84,plain,
! [T_a,T_b,V_f] :
( lhs_atom81(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_filtermap_Osimps_I1_J_0_0,def_lhs_atom81]) ).
fof(def_lhs_atom82,axiom,
! [V_P,T_a] :
( lhs_atom82(V_P,T_a)
<=> c_List_Ofilter(V_P,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_85,plain,
! [T_a,V_P] :
( lhs_atom82(V_P,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_filter_Osimps_I1_J_0_0,def_lhs_atom82]) ).
fof(def_lhs_atom83,axiom,
! [V_x,V_k,T_a] :
( lhs_atom83(V_x,V_k,T_a)
<=> c_List_Olist__update(c_List_Olist_ONil(T_a),V_k,V_x,T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_86,plain,
! [T_a,V_k,V_x] :
( lhs_atom83(V_x,V_k,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_list__update__nonempty_1_0,def_lhs_atom83]) ).
fof(def_lhs_atom84,axiom,
! [V_y,V_i,T_a] :
( lhs_atom84(V_y,V_i,T_a)
<=> c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_y,T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_87,plain,
! [T_a,V_i,V_y] :
( lhs_atom84(V_y,V_i,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_list__update__code_I1_J_0_0,def_lhs_atom84]) ).
fof(def_lhs_atom85,axiom,
! [V_v,V_i,T_a] :
( lhs_atom85(V_v,V_i,T_a)
<=> c_List_Olist__update(c_List_Olist_ONil(T_a),V_i,V_v,T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_88,plain,
! [T_a,V_i,V_v] :
( lhs_atom85(V_v,V_i,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_list__update_Osimps_I1_J_0_0,def_lhs_atom85]) ).
fof(def_lhs_atom86,axiom,
! [V_xa,V_x,T_a] :
( lhs_atom86(V_xa,V_x,T_a)
<=> c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_89,plain,
! [T_a,V_x,V_xa] :
( lhs_atom86(V_xa,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_neq__Nil__conv_1_0,def_lhs_atom86]) ).
fof(def_lhs_atom87,axiom,
! [V_list_H,V_a_H,T_a] :
( lhs_atom87(V_list_H,V_a_H,T_a)
<=> c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_90,plain,
! [T_a,V_a_H,V_list_H] :
( lhs_atom87(V_list_H,V_a_H,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_list_Osimps_I3_J_0_0,def_lhs_atom87]) ).
fof(def_lhs_atom88,axiom,
! [V_x,T_a] :
( lhs_atom88(V_x,T_a)
<=> c_List_Oremove1(V_x,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_91,plain,
! [T_a,V_x] :
( lhs_atom88(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_remove1_Osimps_I1_J_0_0,def_lhs_atom88]) ).
fof(def_lhs_atom89,axiom,
! [V_m,V_as,T_b,T_a] :
( lhs_atom89(V_m,V_as,T_b,T_a)
<=> c_Map_Omap__upds(V_m,V_as,c_List_Olist_ONil(T_b),T_a,T_b) = V_m ),
inference(definition,[],[]) ).
fof(to_be_clausified_92,plain,
! [T_a,T_b,V_as,V_m] :
( lhs_atom89(V_m,V_as,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__upds__Nil2_0_0,def_lhs_atom89]) ).
fof(def_lhs_atom90,axiom,
! [V_m,V_bs,T_b,T_a] :
( lhs_atom90(V_m,V_bs,T_b,T_a)
<=> c_Map_Omap__upds(V_m,c_List_Olist_ONil(T_a),V_bs,T_a,T_b) = V_m ),
inference(definition,[],[]) ).
fof(to_be_clausified_93,plain,
! [T_a,T_b,V_bs,V_m] :
( lhs_atom90(V_m,V_bs,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__upds__Nil1_0_0,def_lhs_atom90]) ).
fof(def_lhs_atom91,axiom,
! [V_f2,V_f1,T_b,T_a] :
( lhs_atom91(V_f2,V_f1,T_b,T_a)
<=> c_List_Olist_Olist__case(V_f1,V_f2,c_List_Olist_ONil(T_b),T_a,T_b) = V_f1 ),
inference(definition,[],[]) ).
fof(to_be_clausified_94,plain,
! [T_a,T_b,V_f1,V_f2] :
( lhs_atom91(V_f2,V_f1,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_list_Osimps_I4_J_0_0,def_lhs_atom91]) ).
fof(def_lhs_atom92,axiom,
! [V_n,T_a] :
( lhs_atom92(V_n,T_a)
<=> c_List_Orotate(V_n,c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_95,plain,
! [T_a,V_n] :
( lhs_atom92(V_n,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rotate__is__Nil__conv_1_0,def_lhs_atom92]) ).
fof(to_be_clausified_96,plain,
! [T_a,T_b,V_f] :
( lhs_atom55(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nil__is__map__conv_1_0,def_lhs_atom55]) ).
fof(def_lhs_atom93,axiom,
! [T_a] :
( lhs_atom93(T_a)
<=> c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_97,plain,
! [T_a] :
( lhs_atom93(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nil__is__append__conv_2_0,def_lhs_atom93]) ).
fof(def_lhs_atom94,axiom,
! [V_r,T_a] :
( lhs_atom94(V_r,T_a)
<=> c_List_Olistrelp(V_r,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_98,plain,
! [T_a,V_r] :
( lhs_atom94(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_listrelp_ONil_0_0,def_lhs_atom94]) ).
fof(def_lhs_atom95,axiom,
! [T_a] :
( lhs_atom95(T_a)
<=> c_List_Orev(c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_99,plain,
! [T_a] :
( lhs_atom95(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rev__is__Nil__conv_1_0,def_lhs_atom95]) ).
fof(def_lhs_atom96,axiom,
! [V_u,V_t,V_s,V_k] :
( lhs_atom96(V_u,V_t,V_s,V_k)
<=> c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_t,V_s,V_k)),c_Lambda_Osubst(V_u,V_s,V_k)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_100,plain,
! [V_k,V_s,V_t,V_u] :
( lhs_atom96(V_u,V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__App_0_0,def_lhs_atom96]) ).
fof(def_lhs_atom97,axiom,
! [V_dB_H,V_dB2,V_dB1] :
( lhs_atom97(V_dB_H,V_dB2,V_dB1)
<=> hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_101,plain,
! [V_dB1,V_dB2,V_dB_H] :
( lhs_atom97(V_dB_H,V_dB2,V_dB1)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I8_J_0_0,def_lhs_atom97]) ).
fof(def_lhs_atom98,axiom,
! [V_dB_H,V_dB2,V_dB1] :
( lhs_atom98(V_dB_H,V_dB2,V_dB1)
<=> c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) ),
inference(definition,[],[]) ).
fof(to_be_clausified_102,plain,
! [V_dB1,V_dB2,V_dB_H] :
( lhs_atom98(V_dB_H,V_dB2,V_dB1)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I9_J_0_0,def_lhs_atom98]) ).
fof(def_lhs_atom99,axiom,
! [V_t,V_s,V_k] :
( lhs_atom99(V_t,V_s,V_k)
<=> c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(V_s,V_k)),c_Lambda_Olift(V_t,V_k)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_103,plain,
! [V_k,V_s,V_t] :
( lhs_atom99(V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_lift_Osimps_I2_J_0_0,def_lhs_atom99]) ).
fof(def_lhs_atom100,axiom,
! [V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a] :
( lhs_atom100(V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a)
<=> c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(V_f2,V_dB1),V_dB2) ),
inference(definition,[],[]) ).
fof(to_be_clausified_104,plain,
! [T_a,V_dB1,V_dB2,V_f1,V_f2,V_f3] :
( lhs_atom100(V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I11_J_0_0,def_lhs_atom100]) ).
fof(def_lhs_atom101,axiom,
! [V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a] :
( lhs_atom101(V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a)
<=> c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_105,plain,
! [T_a,V_dB1,V_dB2,V_f1,V_f2,V_f3] :
( lhs_atom101(V_f3,V_f2,V_f1,V_dB2,V_dB1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Orecs_I2_J_0_0,def_lhs_atom101]) ).
fof(def_lhs_atom102,axiom,
! [V_t,V_s,V_n,V_k] :
( lhs_atom102(V_t,V_s,V_n,V_k)
<=> c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_106,plain,
! [V_k,V_n,V_s,V_t] :
( lhs_atom102(V_t,V_s,V_n,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_liftn_Osimps_I2_J_0_0,def_lhs_atom102]) ).
fof(def_lhs_atom103,axiom,
! [V_u,V_t,V_s,V_k] :
( lhs_atom103(V_u,V_t,V_s,V_k)
<=> c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_107,plain,
! [V_k,V_s,V_t,V_u] :
( lhs_atom103(V_u,V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_substn_Osimps_I2_J_0_0,def_lhs_atom103]) ).
fof(def_lhs_atom104,axiom,
! [V_t] :
( lhs_atom104(V_t)
<=> V_t = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(V_t),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(V_t),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_108,plain,
! [V_t] :
( lhs_atom104(V_t)
| $false ),
inference(fold_definition,[status(thm)],[cls_ex__head__tail_0_0,def_lhs_atom104]) ).
fof(def_lhs_atom105,axiom,
! [V_xs,V_x,V_f,V_a,T_b,T_a] :
( lhs_atom105(V_xs,V_x,V_f,V_a,T_b,T_a)
<=> c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b) ),
inference(definition,[],[]) ).
fof(to_be_clausified_109,plain,
! [T_a,T_b,V_a,V_f,V_x,V_xs] :
( lhs_atom105(V_xs,V_x,V_f,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_foldl__Cons_0_0,def_lhs_atom105]) ).
fof(def_lhs_atom106,axiom,
! [V_ys,V_xs,V_f,V_a,T_b,T_a] :
( lhs_atom106(V_ys,V_xs,V_f,V_a,T_b,T_a)
<=> c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b) ),
inference(definition,[],[]) ).
fof(to_be_clausified_110,plain,
! [T_a,T_b,V_a,V_f,V_xs,V_ys] :
( lhs_atom106(V_ys,V_xs,V_f,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_foldl__append_0_0,def_lhs_atom106]) ).
fof(def_lhs_atom107,axiom,
! [V_nat,V_dB_H] :
( lhs_atom107(V_nat,V_dB_H)
<=> c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_111,plain,
! [V_dB_H,V_nat] :
( lhs_atom107(V_nat,V_dB_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I7_J_0_0,def_lhs_atom107]) ).
fof(def_lhs_atom108,axiom,
! [V_u,V_k] :
( lhs_atom108(V_u,V_k)
<=> c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ),
inference(definition,[],[]) ).
fof(to_be_clausified_112,plain,
! [V_k,V_u] :
( lhs_atom108(V_u,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__eq_0_0,def_lhs_atom108]) ).
fof(def_lhs_atom109,axiom,
! [V_t,V_i] :
( lhs_atom109(V_t,V_i)
<=> ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_113,plain,
! [V_i,V_t] :
( lhs_atom109(V_t,V_i)
| $false ),
inference(fold_definition,[status(thm)],[cls_beta__cases_I1_J_0_0,def_lhs_atom109]) ).
fof(def_lhs_atom110,axiom,
! [V_nat,V_f3,V_f2,V_f1,T_a] :
( lhs_atom110(V_nat,V_f3,V_f2,V_f1,T_a)
<=> c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_114,plain,
! [T_a,V_f1,V_f2,V_f3,V_nat] :
( lhs_atom110(V_nat,V_f3,V_f2,V_f1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Orecs_I1_J_0_0,def_lhs_atom110]) ).
fof(def_lhs_atom111,axiom,
! [V_nat,V_dB_H] :
( lhs_atom111(V_nat,V_dB_H)
<=> c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_115,plain,
! [V_dB_H,V_nat] :
( lhs_atom111(V_nat,V_dB_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I6_J_0_0,def_lhs_atom111]) ).
fof(def_lhs_atom112,axiom,
! [V_nat,V_f3,V_f2,V_f1,T_a] :
( lhs_atom112(V_nat,V_f3,V_f2,V_f1,T_a)
<=> c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_116,plain,
! [T_a,V_f1,V_f2,V_f3,V_nat] :
( lhs_atom112(V_nat,V_f3,V_f2,V_f1,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I10_J_0_0,def_lhs_atom112]) ).
fof(def_lhs_atom113,axiom,
! [V_x,V_env] :
( lhs_atom113(V_x,V_env)
<=> c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_117,plain,
! [V_env,V_x] :
( lhs_atom113(V_x,V_env)
| $false ),
inference(fold_definition,[status(thm)],[cls_typing_OVar_0_0,def_lhs_atom113]) ).
fof(def_lhs_atom114,axiom,
! [V_u,V_ts,V_t] :
( lhs_atom114(V_u,V_ts,V_t)
<=> hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u) = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_ts,c_List_Olist_OCons(V_u,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_118,plain,
! [V_t,V_ts,V_u] :
( lhs_atom114(V_u,V_ts,V_t)
| $false ),
inference(fold_definition,[status(thm)],[cls_app__last_0_0,def_lhs_atom114]) ).
fof(def_lhs_atom115,axiom,
! [V_ts,V_ss,V_r,V_n] :
( lhs_atom115(V_ts,V_ss,V_r,V_n)
<=> c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_119,plain,
! [V_n,V_r,V_ss,V_ts] :
( lhs_atom115(V_ts,V_ss,V_r,V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Var__apps__neq__Abs__apps_0_0,def_lhs_atom115]) ).
fof(def_lhs_atom116,axiom,
! [V_t,V_ss,V_s,V_n] :
( lhs_atom116(V_t,V_ss,V_s,V_n)
<=> hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_120,plain,
! [V_n,V_s,V_ss,V_t] :
( lhs_atom116(V_t,V_ss,V_s,V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Abs__App__neq__Var__apps_0_0,def_lhs_atom116]) ).
fof(def_lhs_atom117,axiom,
! [V_r] :
( lhs_atom117(V_r)
<=> c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_121,plain,
! [V_r] :
( lhs_atom117(V_r)
| $false ),
inference(fold_definition,[status(thm)],[cls_Abs__eq__apps__conv_2_0,def_lhs_atom117]) ).
fof(def_lhs_atom118,axiom,
! [V_r] :
( lhs_atom118(V_r)
<=> c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r) ),
inference(definition,[],[]) ).
fof(to_be_clausified_122,plain,
! [V_r] :
( lhs_atom118(V_r)
| $false ),
inference(fold_definition,[status(thm)],[cls_apps__eq__Abs__conv_2_0,def_lhs_atom118]) ).
fof(def_lhs_atom119,axiom,
! [V_s,V_r] :
( lhs_atom119(V_s,V_r)
<=> hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_123,plain,
! [V_r,V_s] :
( lhs_atom119(V_s,V_r)
| $false ),
inference(fold_definition,[status(thm)],[cls_App__eq__foldl__conv_4_0,def_lhs_atom119]) ).
fof(def_lhs_atom120,axiom,
! [V_nat,V_dB2_H,V_dB1_H] :
( lhs_atom120(V_nat,V_dB2_H,V_dB1_H)
<=> c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ),
inference(definition,[],[]) ).
fof(to_be_clausified_124,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( lhs_atom120(V_nat,V_dB2_H,V_dB1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I4_J_0_0,def_lhs_atom120]) ).
fof(def_lhs_atom121,axiom,
! [V_f,V_a,T_b,T_a] :
( lhs_atom121(V_f,V_a,T_b,T_a)
<=> c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ),
inference(definition,[],[]) ).
fof(to_be_clausified_125,plain,
! [T_a,T_b,V_a,V_f] :
( lhs_atom121(V_f,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_foldl__Nil_0_0,def_lhs_atom121]) ).
fof(def_lhs_atom122,axiom,
! [V_m] :
( lhs_atom122(V_m)
<=> c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition,[],[]) ).
fof(to_be_clausified_126,plain,
! [V_m] :
( lhs_atom122(V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_Var__eq__apps__conv_2_0,def_lhs_atom122]) ).
fof(def_lhs_atom123,axiom,
! [V_nat,V_dB2_H,V_dB1_H] :
( lhs_atom123(V_nat,V_dB2_H,V_dB1_H)
<=> hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_127,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( lhs_atom123(V_nat,V_dB2_H,V_dB1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I5_J_0_0,def_lhs_atom123]) ).
fof(def_lhs_atom124,axiom,
( lhs_atom124
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_128,plain,
( lhs_atom124
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add_0,def_lhs_atom124]) ).
fof(def_lhs_atom125,axiom,
( lhs_atom125
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_129,plain,
( lhs_atom125
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,def_lhs_atom125]) ).
fof(def_lhs_atom126,axiom,
( lhs_atom126
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_130,plain,
( lhs_atom126
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__comm__monoid__add_0,def_lhs_atom126]) ).
fof(def_lhs_atom127,axiom,
( lhs_atom127
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_131,plain,
( lhs_atom127
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add_0,def_lhs_atom127]) ).
fof(def_lhs_atom128,axiom,
( lhs_atom128
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_132,plain,
( lhs_atom128
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__semigroup__add_0,def_lhs_atom128]) ).
fof(def_lhs_atom129,axiom,
( lhs_atom129
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_133,plain,
( lhs_atom129
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom_0,def_lhs_atom129]) ).
fof(def_lhs_atom130,axiom,
( lhs_atom130
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_134,plain,
( lhs_atom130
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1_0,def_lhs_atom130]) ).
fof(def_lhs_atom131,axiom,
( lhs_atom131
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_135,plain,
( lhs_atom131
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__add_0,def_lhs_atom131]) ).
fof(def_lhs_atom132,axiom,
( lhs_atom132
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_136,plain,
( lhs_atom132
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__add_0,def_lhs_atom132]) ).
fof(def_lhs_atom133,axiom,
( lhs_atom133
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_137,plain,
( lhs_atom133
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Osemigroup__add_0,def_lhs_atom133]) ).
fof(def_lhs_atom134,axiom,
( lhs_atom134
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_138,plain,
( lhs_atom134
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add_0,def_lhs_atom134]) ).
fof(def_lhs_atom135,axiom,
( lhs_atom135
<=> class_Orderings_Opreorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_139,plain,
( lhs_atom135
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Opreorder_0,def_lhs_atom135]) ).
fof(def_lhs_atom136,axiom,
( lhs_atom136
<=> class_Orderings_Olinorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_140,plain,
( lhs_atom136
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Olinorder_0,def_lhs_atom136]) ).
fof(def_lhs_atom137,axiom,
( lhs_atom137
<=> class_Orderings_Oorder(tc_nat) ),
inference(definition,[],[]) ).
fof(to_be_clausified_141,plain,
( lhs_atom137
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Oorder_0,def_lhs_atom137]) ).
fof(def_lhs_atom138,axiom,
( lhs_atom138
<=> class_Orderings_Opreorder(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_142,plain,
( lhs_atom138
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Opreorder_0,def_lhs_atom138]) ).
fof(def_lhs_atom139,axiom,
( lhs_atom139
<=> class_Orderings_Oorder(tc_bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_143,plain,
( lhs_atom139
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Oorder_0,def_lhs_atom139]) ).
fof(def_lhs_atom140,axiom,
! [V_x,T_a] :
( lhs_atom140(V_x,T_a)
<=> hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_144,plain,
! [T_a,V_x] :
( lhs_atom140(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0_0,def_lhs_atom140]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X11,X5,X1,X2,X3,X4] :
( lhs_atom106(X11,X5,X1,X2,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_110) ).
fof(c_0_1,axiom,
! [X5,X6,X1,X2,X3,X4] :
( lhs_atom105(X5,X6,X1,X2,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_109) ).
fof(c_0_2,axiom,
! [X27,X17,X18,X36,X37,X4] :
( lhs_atom101(X27,X17,X18,X36,X37,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_105) ).
fof(c_0_3,axiom,
! [X27,X17,X18,X36,X37,X4] :
( lhs_atom100(X27,X17,X18,X36,X37,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_104) ).
fof(c_0_4,axiom,
! [X8,X5,X12,X1,X3,X4] :
( lhs_atom39(X8,X5,X12,X1,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_5,axiom,
! [X16,X17,X18,X2,X3,X4] :
( lhs_atom29(X16,X17,X18,X2,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_6,axiom,
! [X5,X6,X1,X2,X3,X4] :
( lhs_atom18(X5,X6,X1,X2,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_7,axiom,
! [X11,X5,X1,X2,X3,X4] :
( lhs_atom10(X11,X5,X1,X2,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_8,axiom,
! [X38,X27,X17,X18,X4] :
( lhs_atom112(X38,X27,X17,X18,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_116) ).
fof(c_0_9,axiom,
! [X38,X27,X17,X18,X4] :
( lhs_atom110(X38,X27,X17,X18,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_114) ).
fof(c_0_10,axiom,
! [X8,X5,X6,X7,X4] :
( lhs_atom76(X8,X5,X6,X7,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_79) ).
fof(c_0_11,axiom,
! [X27,X17,X18,X28,X4] :
( lhs_atom71(X27,X17,X18,X28,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_74) ).
fof(c_0_12,axiom,
! [X11,X5,X1,X3,X4] :
( lhs_atom70(X11,X5,X1,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_73) ).
fof(c_0_13,axiom,
! [X5,X9,X1,X3,X4] :
( lhs_atom66(X5,X9,X1,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_68) ).
fof(c_0_14,axiom,
! [X27,X17,X18,X28,X4] :
( lhs_atom62(X27,X17,X18,X28,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_64) ).
fof(c_0_15,axiom,
! [X5,X6,X1,X3,X4] :
( lhs_atom28(X5,X6,X1,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_16,axiom,
! [X15,X14,X1,X3,X4] :
( lhs_atom27(X15,X14,X1,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_17,axiom,
! [X14,X6,X1,X3,X4] :
( lhs_atom26(X14,X6,X1,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_18,axiom,
! [X11,X8,X5,X6,X4] :
( lhs_atom25(X11,X8,X5,X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_19,axiom,
! [X6,X9,X1,X3,X4] :
( lhs_atom8(X6,X9,X1,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_20,axiom,
! [X1,X2,X3,X4] :
( lhs_atom121(X1,X2,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_125) ).
fof(c_0_21,axiom,
! [X21,X40,X22,X9] :
( lhs_atom116(X21,X40,X22,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_120) ).
fof(c_0_22,axiom,
! [X30,X40,X13,X9] :
( lhs_atom115(X30,X40,X13,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_119) ).
fof(c_0_23,axiom,
! [X34,X21,X22,X12] :
( lhs_atom103(X34,X21,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_107) ).
fof(c_0_24,axiom,
! [X21,X22,X9,X12] :
( lhs_atom102(X21,X22,X9,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_106) ).
fof(c_0_25,axiom,
! [X34,X21,X22,X12] :
( lhs_atom96(X34,X21,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_100) ).
fof(c_0_26,axiom,
! [X17,X18,X3,X4] :
( lhs_atom91(X17,X18,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_94) ).
fof(c_0_27,axiom,
! [X10,X33,X3,X4] :
( lhs_atom90(X10,X33,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_93) ).
fof(c_0_28,axiom,
! [X10,X32,X3,X4] :
( lhs_atom89(X10,X32,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_92) ).
fof(c_0_29,axiom,
! [X5,X6,X30,X4] :
( lhs_atom80(X5,X6,X30,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_83) ).
fof(c_0_30,axiom,
! [X19,X11,X6,X4] :
( lhs_atom79(X19,X11,X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_82) ).
fof(c_0_31,axiom,
! [X20,X5,X29,X4] :
( lhs_atom78(X20,X5,X29,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_81) ).
fof(c_0_32,axiom,
! [X19,X11,X5,X4] :
( lhs_atom77(X19,X11,X5,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_80) ).
fof(c_0_33,axiom,
! [X5,X1,X3,X4] :
( lhs_atom63(X5,X1,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_65) ).
fof(c_0_34,axiom,
! [X19,X14,X6,X4] :
( lhs_atom57(X19,X14,X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_59) ).
fof(c_0_35,axiom,
! [X11,X5,X6,X4] :
( lhs_atom56(X11,X5,X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_58) ).
fof(c_0_36,axiom,
! [X11,X5,X23,X4] :
( lhs_atom43(X11,X5,X23,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_37,axiom,
! [X8,X5,X6,X4] :
( lhs_atom37(X8,X5,X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_38,axiom,
! [X19,X20,X6,X4] :
( lhs_atom32(X19,X20,X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_39,axiom,
! [X19,X14,X6,X4] :
( lhs_atom31(X19,X14,X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_40,axiom,
! [X5,X6,X9,X4] :
( lhs_atom23(X5,X6,X9,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_41,axiom,
! [X6,X9,X12,X4] :
( lhs_atom15(X6,X9,X12,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_42,axiom,
! [X5,X1,X3,X4] :
( lhs_atom7(X5,X1,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_43,axiom,
! [X5,X6,X7,X4] :
( lhs_atom3(X5,X6,X7,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_44,axiom,
! [X1,X2,X3,X4] :
( lhs_atom1(X1,X2,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_45,axiom,
! [X8,X6,X4] :
( lhs_atom4(X8,X6,X4)
| c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X6,X4) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X8,X4) ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_46,axiom,
! [X38,X41,X42] :
( lhs_atom123(X38,X41,X42)
| ~ $true ),
file('<stdin>',to_be_clausified_127) ).
fof(c_0_47,axiom,
! [X38,X41,X42] :
( lhs_atom120(X38,X41,X42)
| ~ $true ),
file('<stdin>',to_be_clausified_124) ).
fof(c_0_48,axiom,
! [X34,X30,X21] :
( lhs_atom114(X34,X30,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_118) ).
fof(c_0_49,axiom,
! [X21,X22,X12] :
( lhs_atom99(X21,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_103) ).
fof(c_0_50,axiom,
! [X35,X36,X37] :
( lhs_atom98(X35,X36,X37)
| ~ $true ),
file('<stdin>',to_be_clausified_102) ).
fof(c_0_51,axiom,
! [X35,X36,X37] :
( lhs_atom97(X35,X36,X37)
| ~ $true ),
file('<stdin>',to_be_clausified_101) ).
fof(c_0_52,axiom,
! [X1,X3,X4] :
( lhs_atom55(X1,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_96) ).
fof(c_0_53,axiom,
! [X24,X25,X4] :
( lhs_atom87(X24,X25,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_90) ).
fof(c_0_54,axiom,
! [X14,X6,X4] :
( lhs_atom86(X14,X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_89) ).
fof(c_0_55,axiom,
! [X31,X7,X4] :
( lhs_atom85(X31,X7,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_88) ).
fof(c_0_56,axiom,
! [X8,X7,X4] :
( lhs_atom84(X8,X7,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_87) ).
fof(c_0_57,axiom,
! [X6,X12,X4] :
( lhs_atom83(X6,X12,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_86) ).
fof(c_0_58,axiom,
! [X1,X3,X4] :
( lhs_atom81(X1,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_84) ).
fof(c_0_59,axiom,
! [X5,X23,X4] :
( lhs_atom75(X5,X23,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_78) ).
fof(c_0_60,axiom,
! [X5,X6,X4] :
( lhs_atom74(X5,X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_77) ).
fof(c_0_61,axiom,
! [X6,X13,X4] :
( lhs_atom65(X6,X13,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_67) ).
fof(c_0_62,axiom,
! [X13,X2,X4] :
( lhs_atom64(X13,X2,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_66) ).
fof(c_0_63,axiom,
! [X21,X22,X9] :
( lhs_atom61(X21,X22,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_63) ).
fof(c_0_64,axiom,
! [X5,X23,X4] :
( lhs_atom60(X5,X23,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_62) ).
fof(c_0_65,axiom,
! [X5,X6,X4] :
( lhs_atom59(X5,X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_61) ).
fof(c_0_66,axiom,
! [X1,X3,X4] :
( lhs_atom55(X1,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_57) ).
fof(c_0_67,axiom,
! [X5,X13,X4] :
( lhs_atom49(X5,X13,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_49) ).
fof(c_0_68,axiom,
! [X5,X13,X4] :
( lhs_atom48(X5,X13,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_48) ).
fof(c_0_69,axiom,
! [X24,X25,X4] :
( lhs_atom47(X24,X25,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_47) ).
fof(c_0_70,axiom,
! [X11,X5,X4] :
( lhs_atom42(X11,X5,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_71,axiom,
! [X5,X6,X4] :
( lhs_atom38(X5,X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_72,axiom,
! [X5,X6,X4] :
( lhs_atom36(X5,X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_73,axiom,
! [X6,X21,X4] :
( lhs_atom35(X6,X21,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_74,axiom,
! [X21,X22,X12] :
( lhs_atom34(X21,X22,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_75,axiom,
! [X11,X8,X4] :
( lhs_atom33(X11,X8,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_76,axiom,
! [X5,X6,X4] :
( lhs_atom30(X5,X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_77,axiom,
! [X6,X7,X4] :
( lhs_atom24(X6,X7,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_78,axiom,
! [X13,X3,X4] :
( lhs_atom19(X13,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_79,axiom,
! [X6,X9,X4] :
( lhs_atom17(X6,X9,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_80,axiom,
! [X5,X9,X4] :
( lhs_atom12(X5,X9,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_81,axiom,
! [X6,X9,X4] :
( lhs_atom9(X6,X9,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_82,axiom,
! [X6,X4] :
( lhs_atom140(X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_144) ).
fof(c_0_83,axiom,
! [X22,X13] :
( lhs_atom119(X22,X13)
| ~ $true ),
file('<stdin>',to_be_clausified_123) ).
fof(c_0_84,axiom,
! [X6,X39] :
( lhs_atom113(X6,X39)
| ~ $true ),
file('<stdin>',to_be_clausified_117) ).
fof(c_0_85,axiom,
! [X38,X35] :
( lhs_atom111(X38,X35)
| ~ $true ),
file('<stdin>',to_be_clausified_115) ).
fof(c_0_86,axiom,
! [X21,X7] :
( lhs_atom109(X21,X7)
| ~ $true ),
file('<stdin>',to_be_clausified_113) ).
fof(c_0_87,axiom,
! [X34,X12] :
( lhs_atom108(X34,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_112) ).
fof(c_0_88,axiom,
! [X38,X35] :
( lhs_atom107(X38,X35)
| ~ $true ),
file('<stdin>',to_be_clausified_111) ).
fof(c_0_89,axiom,
! [X13,X4] :
( lhs_atom94(X13,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_98) ).
fof(c_0_90,axiom,
! [X9,X4] :
( lhs_atom92(X9,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_95) ).
fof(c_0_91,axiom,
! [X6,X4] :
( lhs_atom88(X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_91) ).
fof(c_0_92,axiom,
! [X23,X4] :
( lhs_atom82(X23,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_85) ).
fof(c_0_93,axiom,
! [X21,X22] :
( lhs_atom73(X21,X22)
| ~ $true ),
file('<stdin>',to_be_clausified_76) ).
fof(c_0_94,axiom,
! [X21,X12] :
( lhs_atom72(X21,X12)
| ~ $true ),
file('<stdin>',to_be_clausified_75) ).
fof(c_0_95,axiom,
! [X21,X22] :
( lhs_atom69(X21,X22)
| ~ $true ),
file('<stdin>',to_be_clausified_72) ).
fof(c_0_96,axiom,
! [X5,X4] :
( lhs_atom67(X5,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_71) ).
fof(c_0_97,axiom,
! [X11,X4] :
( lhs_atom68(X11,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_70) ).
fof(c_0_98,axiom,
! [X5,X4] :
( lhs_atom67(X5,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_69) ).
fof(c_0_99,axiom,
! [X6,X4] :
( lhs_atom58(X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_60) ).
fof(c_0_100,axiom,
! [X26,X4] :
( lhs_atom54(X26,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_56) ).
fof(c_0_101,axiom,
! [X5,X4] :
( lhs_atom52(X5,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_55) ).
fof(c_0_102,axiom,
! [X6,X4] :
( lhs_atom53(X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_54) ).
fof(c_0_103,axiom,
! [X5,X4] :
( lhs_atom52(X5,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_53) ).
fof(c_0_104,axiom,
! [X11,X4] :
( lhs_atom51(X11,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_52) ).
fof(c_0_105,axiom,
! [X11,X4] :
( lhs_atom51(X11,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_51) ).
fof(c_0_106,axiom,
! [X13,X4] :
( lhs_atom41(X13,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_107,axiom,
! [X6,X4] :
( lhs_atom40(X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_108,axiom,
! [X6,X4] :
( lhs_atom21(X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_109,axiom,
! [X6,X4] :
( lhs_atom21(X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_110,axiom,
! [X5,X4] :
( lhs_atom20(X5,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_111,axiom,
! [X10] :
( lhs_atom122(X10)
| ~ $true ),
file('<stdin>',to_be_clausified_126) ).
fof(c_0_112,axiom,
! [X13] :
( lhs_atom118(X13)
| ~ $true ),
file('<stdin>',to_be_clausified_122) ).
fof(c_0_113,axiom,
! [X13] :
( lhs_atom117(X13)
| ~ $true ),
file('<stdin>',to_be_clausified_121) ).
fof(c_0_114,axiom,
! [X21] :
( lhs_atom104(X21)
| ~ $true ),
file('<stdin>',to_be_clausified_108) ).
fof(c_0_115,axiom,
! [X4] :
( lhs_atom95(X4)
| ~ $true ),
file('<stdin>',to_be_clausified_99) ).
fof(c_0_116,axiom,
! [X4] :
( lhs_atom93(X4)
| ~ $true ),
file('<stdin>',to_be_clausified_97) ).
fof(c_0_117,axiom,
! [X4] :
( lhs_atom50(X4)
| ~ $true ),
file('<stdin>',to_be_clausified_50) ).
fof(c_0_118,axiom,
! [X4] :
( lhs_atom46(X4)
| ~ $true ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_119,axiom,
! [X4] :
( lhs_atom45(X4)
| ~ $true ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_120,axiom,
! [X4] :
( lhs_atom44(X4)
| ~ $true ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_121,axiom,
! [X4] :
( lhs_atom22(X4)
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_122,axiom,
! [X9] :
( lhs_atom14(X9)
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_123,axiom,
! [X6] :
( lhs_atom13(X6)
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_124,axiom,
! [X4] :
( lhs_atom11(X4)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_125,axiom,
! [X10] :
( lhs_atom6(X10)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_126,axiom,
! [X9] :
( lhs_atom5(X9)
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_127,axiom,
! [X4] :
( lhs_atom2(X4)
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_128,axiom,
( lhs_atom139
| ~ $true ),
file('<stdin>',to_be_clausified_143) ).
fof(c_0_129,axiom,
( lhs_atom138
| ~ $true ),
file('<stdin>',to_be_clausified_142) ).
fof(c_0_130,axiom,
( lhs_atom137
| ~ $true ),
file('<stdin>',to_be_clausified_141) ).
fof(c_0_131,axiom,
( lhs_atom136
| ~ $true ),
file('<stdin>',to_be_clausified_140) ).
fof(c_0_132,axiom,
( lhs_atom135
| ~ $true ),
file('<stdin>',to_be_clausified_139) ).
fof(c_0_133,axiom,
( lhs_atom134
| ~ $true ),
file('<stdin>',to_be_clausified_138) ).
fof(c_0_134,axiom,
( lhs_atom133
| ~ $true ),
file('<stdin>',to_be_clausified_137) ).
fof(c_0_135,axiom,
( lhs_atom132
| ~ $true ),
file('<stdin>',to_be_clausified_136) ).
fof(c_0_136,axiom,
( lhs_atom131
| ~ $true ),
file('<stdin>',to_be_clausified_135) ).
fof(c_0_137,axiom,
( lhs_atom130
| ~ $true ),
file('<stdin>',to_be_clausified_134) ).
fof(c_0_138,axiom,
( lhs_atom129
| ~ $true ),
file('<stdin>',to_be_clausified_133) ).
fof(c_0_139,axiom,
( lhs_atom128
| ~ $true ),
file('<stdin>',to_be_clausified_132) ).
fof(c_0_140,axiom,
( lhs_atom127
| ~ $true ),
file('<stdin>',to_be_clausified_131) ).
fof(c_0_141,axiom,
( lhs_atom126
| ~ $true ),
file('<stdin>',to_be_clausified_130) ).
fof(c_0_142,axiom,
( lhs_atom125
| ~ $true ),
file('<stdin>',to_be_clausified_129) ).
fof(c_0_143,axiom,
( lhs_atom124
| ~ $true ),
file('<stdin>',to_be_clausified_128) ).
fof(c_0_144,axiom,
( lhs_atom16
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_145,plain,
! [X11,X5,X1,X2,X3,X4] : lhs_atom106(X11,X5,X1,X2,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_146,plain,
! [X5,X6,X1,X2,X3,X4] : lhs_atom105(X5,X6,X1,X2,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_147,plain,
! [X27,X17,X18,X36,X37,X4] : lhs_atom101(X27,X17,X18,X36,X37,X4),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_148,plain,
! [X27,X17,X18,X36,X37,X4] : lhs_atom100(X27,X17,X18,X36,X37,X4),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_149,plain,
! [X8,X5,X12,X1,X3,X4] : lhs_atom39(X8,X5,X12,X1,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_150,plain,
! [X16,X17,X18,X2,X3,X4] : lhs_atom29(X16,X17,X18,X2,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_151,plain,
! [X5,X6,X1,X2,X3,X4] : lhs_atom18(X5,X6,X1,X2,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_152,plain,
! [X11,X5,X1,X2,X3,X4] : lhs_atom10(X11,X5,X1,X2,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_153,plain,
! [X38,X27,X17,X18,X4] : lhs_atom112(X38,X27,X17,X18,X4),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_154,plain,
! [X38,X27,X17,X18,X4] : lhs_atom110(X38,X27,X17,X18,X4),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_155,plain,
! [X8,X5,X6,X7,X4] : lhs_atom76(X8,X5,X6,X7,X4),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_156,plain,
! [X27,X17,X18,X28,X4] : lhs_atom71(X27,X17,X18,X28,X4),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_157,plain,
! [X11,X5,X1,X3,X4] : lhs_atom70(X11,X5,X1,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_158,plain,
! [X5,X9,X1,X3,X4] : lhs_atom66(X5,X9,X1,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_159,plain,
! [X27,X17,X18,X28,X4] : lhs_atom62(X27,X17,X18,X28,X4),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_160,plain,
! [X5,X6,X1,X3,X4] : lhs_atom28(X5,X6,X1,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_161,plain,
! [X15,X14,X1,X3,X4] : lhs_atom27(X15,X14,X1,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_162,plain,
! [X14,X6,X1,X3,X4] : lhs_atom26(X14,X6,X1,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_163,plain,
! [X11,X8,X5,X6,X4] : lhs_atom25(X11,X8,X5,X6,X4),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_164,plain,
! [X6,X9,X1,X3,X4] : lhs_atom8(X6,X9,X1,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_165,plain,
! [X1,X2,X3,X4] : lhs_atom121(X1,X2,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_166,plain,
! [X21,X40,X22,X9] : lhs_atom116(X21,X40,X22,X9),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_167,plain,
! [X30,X40,X13,X9] : lhs_atom115(X30,X40,X13,X9),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_168,plain,
! [X34,X21,X22,X12] : lhs_atom103(X34,X21,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_169,plain,
! [X21,X22,X9,X12] : lhs_atom102(X21,X22,X9,X12),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_170,plain,
! [X34,X21,X22,X12] : lhs_atom96(X34,X21,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_171,plain,
! [X17,X18,X3,X4] : lhs_atom91(X17,X18,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_172,plain,
! [X10,X33,X3,X4] : lhs_atom90(X10,X33,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_173,plain,
! [X10,X32,X3,X4] : lhs_atom89(X10,X32,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_174,plain,
! [X5,X6,X30,X4] : lhs_atom80(X5,X6,X30,X4),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_175,plain,
! [X19,X11,X6,X4] : lhs_atom79(X19,X11,X6,X4),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_176,plain,
! [X20,X5,X29,X4] : lhs_atom78(X20,X5,X29,X4),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_177,plain,
! [X19,X11,X5,X4] : lhs_atom77(X19,X11,X5,X4),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_178,plain,
! [X5,X1,X3,X4] : lhs_atom63(X5,X1,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_179,plain,
! [X19,X14,X6,X4] : lhs_atom57(X19,X14,X6,X4),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_180,plain,
! [X11,X5,X6,X4] : lhs_atom56(X11,X5,X6,X4),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_181,plain,
! [X11,X5,X23,X4] : lhs_atom43(X11,X5,X23,X4),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_182,plain,
! [X8,X5,X6,X4] : lhs_atom37(X8,X5,X6,X4),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_183,plain,
! [X19,X20,X6,X4] : lhs_atom32(X19,X20,X6,X4),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_184,plain,
! [X19,X14,X6,X4] : lhs_atom31(X19,X14,X6,X4),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_185,plain,
! [X5,X6,X9,X4] : lhs_atom23(X5,X6,X9,X4),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_186,plain,
! [X6,X9,X12,X4] : lhs_atom15(X6,X9,X12,X4),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_187,plain,
! [X5,X1,X3,X4] : lhs_atom7(X5,X1,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_188,plain,
! [X5,X6,X7,X4] : lhs_atom3(X5,X6,X7,X4),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_189,plain,
! [X1,X2,X3,X4] : lhs_atom1(X1,X2,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_190,axiom,
! [X8,X6,X4] :
( lhs_atom4(X8,X6,X4)
| c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X6,X4) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X8,X4) ),
c_0_45 ).
fof(c_0_191,plain,
! [X38,X41,X42] : lhs_atom123(X38,X41,X42),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_192,plain,
! [X38,X41,X42] : lhs_atom120(X38,X41,X42),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_193,plain,
! [X34,X30,X21] : lhs_atom114(X34,X30,X21),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_194,plain,
! [X21,X22,X12] : lhs_atom99(X21,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_195,plain,
! [X35,X36,X37] : lhs_atom98(X35,X36,X37),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_196,plain,
! [X35,X36,X37] : lhs_atom97(X35,X36,X37),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_197,plain,
! [X1,X3,X4] : lhs_atom55(X1,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_198,plain,
! [X24,X25,X4] : lhs_atom87(X24,X25,X4),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_199,plain,
! [X14,X6,X4] : lhs_atom86(X14,X6,X4),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_200,plain,
! [X31,X7,X4] : lhs_atom85(X31,X7,X4),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_201,plain,
! [X8,X7,X4] : lhs_atom84(X8,X7,X4),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_202,plain,
! [X6,X12,X4] : lhs_atom83(X6,X12,X4),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_203,plain,
! [X1,X3,X4] : lhs_atom81(X1,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_204,plain,
! [X5,X23,X4] : lhs_atom75(X5,X23,X4),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_205,plain,
! [X5,X6,X4] : lhs_atom74(X5,X6,X4),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_206,plain,
! [X6,X13,X4] : lhs_atom65(X6,X13,X4),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_207,plain,
! [X13,X2,X4] : lhs_atom64(X13,X2,X4),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_208,plain,
! [X21,X22,X9] : lhs_atom61(X21,X22,X9),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_209,plain,
! [X5,X23,X4] : lhs_atom60(X5,X23,X4),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_210,plain,
! [X5,X6,X4] : lhs_atom59(X5,X6,X4),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_211,plain,
! [X1,X3,X4] : lhs_atom55(X1,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_212,plain,
! [X5,X13,X4] : lhs_atom49(X5,X13,X4),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_213,plain,
! [X5,X13,X4] : lhs_atom48(X5,X13,X4),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_214,plain,
! [X24,X25,X4] : lhs_atom47(X24,X25,X4),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_215,plain,
! [X11,X5,X4] : lhs_atom42(X11,X5,X4),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_216,plain,
! [X5,X6,X4] : lhs_atom38(X5,X6,X4),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_217,plain,
! [X5,X6,X4] : lhs_atom36(X5,X6,X4),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_218,plain,
! [X6,X21,X4] : lhs_atom35(X6,X21,X4),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_219,plain,
! [X21,X22,X12] : lhs_atom34(X21,X22,X12),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_220,plain,
! [X11,X8,X4] : lhs_atom33(X11,X8,X4),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_221,plain,
! [X5,X6,X4] : lhs_atom30(X5,X6,X4),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_222,plain,
! [X6,X7,X4] : lhs_atom24(X6,X7,X4),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_223,plain,
! [X13,X3,X4] : lhs_atom19(X13,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_224,plain,
! [X6,X9,X4] : lhs_atom17(X6,X9,X4),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_225,plain,
! [X5,X9,X4] : lhs_atom12(X5,X9,X4),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_226,plain,
! [X6,X9,X4] : lhs_atom9(X6,X9,X4),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_227,plain,
! [X6,X4] : lhs_atom140(X6,X4),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_228,plain,
! [X22,X13] : lhs_atom119(X22,X13),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_229,plain,
! [X6,X39] : lhs_atom113(X6,X39),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_230,plain,
! [X38,X35] : lhs_atom111(X38,X35),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_231,plain,
! [X21,X7] : lhs_atom109(X21,X7),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_232,plain,
! [X34,X12] : lhs_atom108(X34,X12),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_233,plain,
! [X38,X35] : lhs_atom107(X38,X35),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_234,plain,
! [X13,X4] : lhs_atom94(X13,X4),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_235,plain,
! [X9,X4] : lhs_atom92(X9,X4),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_236,plain,
! [X6,X4] : lhs_atom88(X6,X4),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_237,plain,
! [X23,X4] : lhs_atom82(X23,X4),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_238,plain,
! [X21,X22] : lhs_atom73(X21,X22),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_239,plain,
! [X21,X12] : lhs_atom72(X21,X12),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_240,plain,
! [X21,X22] : lhs_atom69(X21,X22),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_241,plain,
! [X5,X4] : lhs_atom67(X5,X4),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_242,plain,
! [X11,X4] : lhs_atom68(X11,X4),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_243,plain,
! [X5,X4] : lhs_atom67(X5,X4),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_244,plain,
! [X6,X4] : lhs_atom58(X6,X4),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_245,plain,
! [X26,X4] : lhs_atom54(X26,X4),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_246,plain,
! [X5,X4] : lhs_atom52(X5,X4),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_247,plain,
! [X6,X4] : lhs_atom53(X6,X4),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_248,plain,
! [X5,X4] : lhs_atom52(X5,X4),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_249,plain,
! [X11,X4] : lhs_atom51(X11,X4),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_250,plain,
! [X11,X4] : lhs_atom51(X11,X4),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_251,plain,
! [X13,X4] : lhs_atom41(X13,X4),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_252,plain,
! [X6,X4] : lhs_atom40(X6,X4),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_253,plain,
! [X6,X4] : lhs_atom21(X6,X4),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_254,plain,
! [X6,X4] : lhs_atom21(X6,X4),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_255,plain,
! [X5,X4] : lhs_atom20(X5,X4),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_256,plain,
! [X10] : lhs_atom122(X10),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_257,plain,
! [X13] : lhs_atom118(X13),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_258,plain,
! [X13] : lhs_atom117(X13),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_259,plain,
! [X21] : lhs_atom104(X21),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_260,plain,
! [X4] : lhs_atom95(X4),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_261,plain,
! [X4] : lhs_atom93(X4),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_262,plain,
! [X4] : lhs_atom50(X4),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_263,plain,
! [X4] : lhs_atom46(X4),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_264,plain,
! [X4] : lhs_atom45(X4),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_265,plain,
! [X4] : lhs_atom44(X4),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_266,plain,
! [X4] : lhs_atom22(X4),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_267,plain,
! [X9] : lhs_atom14(X9),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_268,plain,
! [X6] : lhs_atom13(X6),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_269,plain,
! [X4] : lhs_atom11(X4),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_270,plain,
! [X10] : lhs_atom6(X10),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_271,plain,
! [X9] : lhs_atom5(X9),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_272,plain,
! [X4] : lhs_atom2(X4),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_273,plain,
lhs_atom139,
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_274,plain,
lhs_atom138,
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_275,plain,
lhs_atom137,
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_276,plain,
lhs_atom136,
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_277,plain,
lhs_atom135,
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_278,plain,
lhs_atom134,
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_279,plain,
lhs_atom133,
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_280,plain,
lhs_atom132,
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_281,plain,
lhs_atom131,
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_282,plain,
lhs_atom130,
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_283,plain,
lhs_atom129,
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_284,plain,
lhs_atom128,
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_285,plain,
lhs_atom127,
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_286,plain,
lhs_atom126,
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_287,plain,
lhs_atom125,
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_288,plain,
lhs_atom124,
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_289,plain,
lhs_atom16,
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_290,plain,
! [X12,X13,X14,X15,X16,X17] : lhs_atom106(X12,X13,X14,X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_145]) ).
fof(c_0_291,plain,
! [X7,X8,X9,X10,X11,X12] : lhs_atom105(X7,X8,X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_146]) ).
fof(c_0_292,plain,
! [X38,X39,X40,X41,X42,X43] : lhs_atom101(X38,X39,X40,X41,X42,X43),
inference(variable_rename,[status(thm)],[c_0_147]) ).
fof(c_0_293,plain,
! [X38,X39,X40,X41,X42,X43] : lhs_atom100(X38,X39,X40,X41,X42,X43),
inference(variable_rename,[status(thm)],[c_0_148]) ).
fof(c_0_294,plain,
! [X13,X14,X15,X16,X17,X18] : lhs_atom39(X13,X14,X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_149]) ).
fof(c_0_295,plain,
! [X19,X20,X21,X22,X23,X24] : lhs_atom29(X19,X20,X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_150]) ).
fof(c_0_296,plain,
! [X7,X8,X9,X10,X11,X12] : lhs_atom18(X7,X8,X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_151]) ).
fof(c_0_297,plain,
! [X12,X13,X14,X15,X16,X17] : lhs_atom10(X12,X13,X14,X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_152]) ).
fof(c_0_298,plain,
! [X39,X40,X41,X42,X43] : lhs_atom112(X39,X40,X41,X42,X43),
inference(variable_rename,[status(thm)],[c_0_153]) ).
fof(c_0_299,plain,
! [X39,X40,X41,X42,X43] : lhs_atom110(X39,X40,X41,X42,X43),
inference(variable_rename,[status(thm)],[c_0_154]) ).
fof(c_0_300,plain,
! [X9,X10,X11,X12,X13] : lhs_atom76(X9,X10,X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_155]) ).
fof(c_0_301,plain,
! [X29,X30,X31,X32,X33] : lhs_atom71(X29,X30,X31,X32,X33),
inference(variable_rename,[status(thm)],[c_0_156]) ).
fof(c_0_302,plain,
! [X12,X13,X14,X15,X16] : lhs_atom70(X12,X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_157]) ).
fof(c_0_303,plain,
! [X10,X11,X12,X13,X14] : lhs_atom66(X10,X11,X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_158]) ).
fof(c_0_304,plain,
! [X29,X30,X31,X32,X33] : lhs_atom62(X29,X30,X31,X32,X33),
inference(variable_rename,[status(thm)],[c_0_159]) ).
fof(c_0_305,plain,
! [X7,X8,X9,X10,X11] : lhs_atom28(X7,X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_160]) ).
fof(c_0_306,plain,
! [X16,X17,X18,X19,X20] : lhs_atom27(X16,X17,X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_161]) ).
fof(c_0_307,plain,
! [X15,X16,X17,X18,X19] : lhs_atom26(X15,X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_162]) ).
fof(c_0_308,plain,
! [X12,X13,X14,X15,X16] : lhs_atom25(X12,X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_163]) ).
fof(c_0_309,plain,
! [X10,X11,X12,X13,X14] : lhs_atom8(X10,X11,X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_164]) ).
fof(c_0_310,plain,
! [X5,X6,X7,X8] : lhs_atom121(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_165]) ).
fof(c_0_311,plain,
! [X41,X42,X43,X44] : lhs_atom116(X41,X42,X43,X44),
inference(variable_rename,[status(thm)],[c_0_166]) ).
fof(c_0_312,plain,
! [X41,X42,X43,X44] : lhs_atom115(X41,X42,X43,X44),
inference(variable_rename,[status(thm)],[c_0_167]) ).
fof(c_0_313,plain,
! [X35,X36,X37,X38] : lhs_atom103(X35,X36,X37,X38),
inference(variable_rename,[status(thm)],[c_0_168]) ).
fof(c_0_314,plain,
! [X23,X24,X25,X26] : lhs_atom102(X23,X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_169]) ).
fof(c_0_315,plain,
! [X35,X36,X37,X38] : lhs_atom96(X35,X36,X37,X38),
inference(variable_rename,[status(thm)],[c_0_170]) ).
fof(c_0_316,plain,
! [X19,X20,X21,X22] : lhs_atom91(X19,X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_171]) ).
fof(c_0_317,plain,
! [X34,X35,X36,X37] : lhs_atom90(X34,X35,X36,X37),
inference(variable_rename,[status(thm)],[c_0_172]) ).
fof(c_0_318,plain,
! [X33,X34,X35,X36] : lhs_atom89(X33,X34,X35,X36),
inference(variable_rename,[status(thm)],[c_0_173]) ).
fof(c_0_319,plain,
! [X31,X32,X33,X34] : lhs_atom80(X31,X32,X33,X34),
inference(variable_rename,[status(thm)],[c_0_174]) ).
fof(c_0_320,plain,
! [X20,X21,X22,X23] : lhs_atom79(X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_175]) ).
fof(c_0_321,plain,
! [X30,X31,X32,X33] : lhs_atom78(X30,X31,X32,X33),
inference(variable_rename,[status(thm)],[c_0_176]) ).
fof(c_0_322,plain,
! [X20,X21,X22,X23] : lhs_atom77(X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_177]) ).
fof(c_0_323,plain,
! [X6,X7,X8,X9] : lhs_atom63(X6,X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_178]) ).
fof(c_0_324,plain,
! [X20,X21,X22,X23] : lhs_atom57(X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_179]) ).
fof(c_0_325,plain,
! [X12,X13,X14,X15] : lhs_atom56(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_180]) ).
fof(c_0_326,plain,
! [X24,X25,X26,X27] : lhs_atom43(X24,X25,X26,X27),
inference(variable_rename,[status(thm)],[c_0_181]) ).
fof(c_0_327,plain,
! [X9,X10,X11,X12] : lhs_atom37(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_182]) ).
fof(c_0_328,plain,
! [X21,X22,X23,X24] : lhs_atom32(X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_183]) ).
fof(c_0_329,plain,
! [X20,X21,X22,X23] : lhs_atom31(X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_184]) ).
fof(c_0_330,plain,
! [X10,X11,X12,X13] : lhs_atom23(X10,X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_185]) ).
fof(c_0_331,plain,
! [X13,X14,X15,X16] : lhs_atom15(X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_186]) ).
fof(c_0_332,plain,
! [X6,X7,X8,X9] : lhs_atom7(X6,X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_187]) ).
fof(c_0_333,plain,
! [X8,X9,X10,X11] : lhs_atom3(X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_188]) ).
fof(c_0_334,plain,
! [X5,X6,X7,X8] : lhs_atom1(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_189]) ).
fof(c_0_335,plain,
! [X9,X10,X11] :
( lhs_atom4(X9,X10,X11)
| c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X10,X11) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_190]) ).
fof(c_0_336,plain,
! [X43,X44,X45] : lhs_atom123(X43,X44,X45),
inference(variable_rename,[status(thm)],[c_0_191]) ).
fof(c_0_337,plain,
! [X43,X44,X45] : lhs_atom120(X43,X44,X45),
inference(variable_rename,[status(thm)],[c_0_192]) ).
fof(c_0_338,plain,
! [X35,X36,X37] : lhs_atom114(X35,X36,X37),
inference(variable_rename,[status(thm)],[c_0_193]) ).
fof(c_0_339,plain,
! [X23,X24,X25] : lhs_atom99(X23,X24,X25),
inference(variable_rename,[status(thm)],[c_0_194]) ).
fof(c_0_340,plain,
! [X38,X39,X40] : lhs_atom98(X38,X39,X40),
inference(variable_rename,[status(thm)],[c_0_195]) ).
fof(c_0_341,plain,
! [X38,X39,X40] : lhs_atom97(X38,X39,X40),
inference(variable_rename,[status(thm)],[c_0_196]) ).
fof(c_0_342,plain,
! [X5,X6,X7] : lhs_atom55(X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_343,plain,
! [X26,X27,X28] : lhs_atom87(X26,X27,X28),
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_344,plain,
! [X15,X16,X17] : lhs_atom86(X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_199]) ).
fof(c_0_345,plain,
! [X32,X33,X34] : lhs_atom85(X32,X33,X34),
inference(variable_rename,[status(thm)],[c_0_200]) ).
fof(c_0_346,plain,
! [X9,X10,X11] : lhs_atom84(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_347,plain,
! [X13,X14,X15] : lhs_atom83(X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_202]) ).
fof(c_0_348,plain,
! [X5,X6,X7] : lhs_atom81(X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_203]) ).
fof(c_0_349,plain,
! [X24,X25,X26] : lhs_atom75(X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_204]) ).
fof(c_0_350,plain,
! [X7,X8,X9] : lhs_atom74(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_205]) ).
fof(c_0_351,plain,
! [X14,X15,X16] : lhs_atom65(X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_352,plain,
! [X14,X15,X16] : lhs_atom64(X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_353,plain,
! [X23,X24,X25] : lhs_atom61(X23,X24,X25),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_354,plain,
! [X24,X25,X26] : lhs_atom60(X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_355,plain,
! [X7,X8,X9] : lhs_atom59(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_210]) ).
fof(c_0_356,plain,
! [X5,X6,X7] : lhs_atom55(X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_211]) ).
fof(c_0_357,plain,
! [X14,X15,X16] : lhs_atom49(X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_212]) ).
fof(c_0_358,plain,
! [X14,X15,X16] : lhs_atom48(X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_213]) ).
fof(c_0_359,plain,
! [X26,X27,X28] : lhs_atom47(X26,X27,X28),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_360,plain,
! [X12,X13,X14] : lhs_atom42(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_215]) ).
fof(c_0_361,plain,
! [X7,X8,X9] : lhs_atom38(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_216]) ).
fof(c_0_362,plain,
! [X7,X8,X9] : lhs_atom36(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_217]) ).
fof(c_0_363,plain,
! [X22,X23,X24] : lhs_atom35(X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_218]) ).
fof(c_0_364,plain,
! [X23,X24,X25] : lhs_atom34(X23,X24,X25),
inference(variable_rename,[status(thm)],[c_0_219]) ).
fof(c_0_365,plain,
! [X12,X13,X14] : lhs_atom33(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_220]) ).
fof(c_0_366,plain,
! [X7,X8,X9] : lhs_atom30(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_221]) ).
fof(c_0_367,plain,
! [X8,X9,X10] : lhs_atom24(X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_222]) ).
fof(c_0_368,plain,
! [X14,X15,X16] : lhs_atom19(X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_223]) ).
fof(c_0_369,plain,
! [X10,X11,X12] : lhs_atom17(X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_224]) ).
fof(c_0_370,plain,
! [X10,X11,X12] : lhs_atom12(X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_225]) ).
fof(c_0_371,plain,
! [X10,X11,X12] : lhs_atom9(X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_226]) ).
fof(c_0_372,plain,
! [X7,X8] : lhs_atom140(X7,X8),
inference(variable_rename,[status(thm)],[c_0_227]) ).
fof(c_0_373,plain,
! [X23,X24] : lhs_atom119(X23,X24),
inference(variable_rename,[status(thm)],[c_0_228]) ).
fof(c_0_374,plain,
! [X40,X41] : lhs_atom113(X40,X41),
inference(variable_rename,[status(thm)],[c_0_229]) ).
fof(c_0_375,plain,
! [X39,X40] : lhs_atom111(X39,X40),
inference(variable_rename,[status(thm)],[c_0_230]) ).
fof(c_0_376,plain,
! [X22,X23] : lhs_atom109(X22,X23),
inference(variable_rename,[status(thm)],[c_0_231]) ).
fof(c_0_377,plain,
! [X35,X36] : lhs_atom108(X35,X36),
inference(variable_rename,[status(thm)],[c_0_232]) ).
fof(c_0_378,plain,
! [X39,X40] : lhs_atom107(X39,X40),
inference(variable_rename,[status(thm)],[c_0_233]) ).
fof(c_0_379,plain,
! [X14,X15] : lhs_atom94(X14,X15),
inference(variable_rename,[status(thm)],[c_0_234]) ).
fof(c_0_380,plain,
! [X10,X11] : lhs_atom92(X10,X11),
inference(variable_rename,[status(thm)],[c_0_235]) ).
fof(c_0_381,plain,
! [X7,X8] : lhs_atom88(X7,X8),
inference(variable_rename,[status(thm)],[c_0_236]) ).
fof(c_0_382,plain,
! [X24,X25] : lhs_atom82(X24,X25),
inference(variable_rename,[status(thm)],[c_0_237]) ).
fof(c_0_383,plain,
! [X23,X24] : lhs_atom73(X23,X24),
inference(variable_rename,[status(thm)],[c_0_238]) ).
fof(c_0_384,plain,
! [X22,X23] : lhs_atom72(X22,X23),
inference(variable_rename,[status(thm)],[c_0_239]) ).
fof(c_0_385,plain,
! [X23,X24] : lhs_atom69(X23,X24),
inference(variable_rename,[status(thm)],[c_0_240]) ).
fof(c_0_386,plain,
! [X6,X7] : lhs_atom67(X6,X7),
inference(variable_rename,[status(thm)],[c_0_241]) ).
fof(c_0_387,plain,
! [X12,X13] : lhs_atom68(X12,X13),
inference(variable_rename,[status(thm)],[c_0_242]) ).
fof(c_0_388,plain,
! [X6,X7] : lhs_atom67(X6,X7),
inference(variable_rename,[status(thm)],[c_0_243]) ).
fof(c_0_389,plain,
! [X7,X8] : lhs_atom58(X7,X8),
inference(variable_rename,[status(thm)],[c_0_244]) ).
fof(c_0_390,plain,
! [X27,X28] : lhs_atom54(X27,X28),
inference(variable_rename,[status(thm)],[c_0_245]) ).
fof(c_0_391,plain,
! [X6,X7] : lhs_atom52(X6,X7),
inference(variable_rename,[status(thm)],[c_0_246]) ).
fof(c_0_392,plain,
! [X7,X8] : lhs_atom53(X7,X8),
inference(variable_rename,[status(thm)],[c_0_247]) ).
fof(c_0_393,plain,
! [X6,X7] : lhs_atom52(X6,X7),
inference(variable_rename,[status(thm)],[c_0_248]) ).
fof(c_0_394,plain,
! [X12,X13] : lhs_atom51(X12,X13),
inference(variable_rename,[status(thm)],[c_0_249]) ).
fof(c_0_395,plain,
! [X12,X13] : lhs_atom51(X12,X13),
inference(variable_rename,[status(thm)],[c_0_250]) ).
fof(c_0_396,plain,
! [X14,X15] : lhs_atom41(X14,X15),
inference(variable_rename,[status(thm)],[c_0_251]) ).
fof(c_0_397,plain,
! [X7,X8] : lhs_atom40(X7,X8),
inference(variable_rename,[status(thm)],[c_0_252]) ).
fof(c_0_398,plain,
! [X7,X8] : lhs_atom21(X7,X8),
inference(variable_rename,[status(thm)],[c_0_253]) ).
fof(c_0_399,plain,
! [X7,X8] : lhs_atom21(X7,X8),
inference(variable_rename,[status(thm)],[c_0_254]) ).
fof(c_0_400,plain,
! [X6,X7] : lhs_atom20(X6,X7),
inference(variable_rename,[status(thm)],[c_0_255]) ).
fof(c_0_401,plain,
! [X11] : lhs_atom122(X11),
inference(variable_rename,[status(thm)],[c_0_256]) ).
fof(c_0_402,plain,
! [X14] : lhs_atom118(X14),
inference(variable_rename,[status(thm)],[c_0_257]) ).
fof(c_0_403,plain,
! [X14] : lhs_atom117(X14),
inference(variable_rename,[status(thm)],[c_0_258]) ).
fof(c_0_404,plain,
! [X22] : lhs_atom104(X22),
inference(variable_rename,[status(thm)],[c_0_259]) ).
fof(c_0_405,plain,
! [X5] : lhs_atom95(X5),
inference(variable_rename,[status(thm)],[c_0_260]) ).
fof(c_0_406,plain,
! [X5] : lhs_atom93(X5),
inference(variable_rename,[status(thm)],[c_0_261]) ).
fof(c_0_407,plain,
! [X5] : lhs_atom50(X5),
inference(variable_rename,[status(thm)],[c_0_262]) ).
fof(c_0_408,plain,
! [X5] : lhs_atom46(X5),
inference(variable_rename,[status(thm)],[c_0_263]) ).
fof(c_0_409,plain,
! [X5] : lhs_atom45(X5),
inference(variable_rename,[status(thm)],[c_0_264]) ).
fof(c_0_410,plain,
! [X5] : lhs_atom44(X5),
inference(variable_rename,[status(thm)],[c_0_265]) ).
fof(c_0_411,plain,
! [X5] : lhs_atom22(X5),
inference(variable_rename,[status(thm)],[c_0_266]) ).
fof(c_0_412,plain,
! [X10] : lhs_atom14(X10),
inference(variable_rename,[status(thm)],[c_0_267]) ).
fof(c_0_413,plain,
! [X7] : lhs_atom13(X7),
inference(variable_rename,[status(thm)],[c_0_268]) ).
fof(c_0_414,plain,
! [X5] : lhs_atom11(X5),
inference(variable_rename,[status(thm)],[c_0_269]) ).
fof(c_0_415,plain,
! [X11] : lhs_atom6(X11),
inference(variable_rename,[status(thm)],[c_0_270]) ).
fof(c_0_416,plain,
! [X10] : lhs_atom5(X10),
inference(variable_rename,[status(thm)],[c_0_271]) ).
fof(c_0_417,plain,
! [X5] : lhs_atom2(X5),
inference(variable_rename,[status(thm)],[c_0_272]) ).
fof(c_0_418,plain,
lhs_atom139,
c_0_273 ).
fof(c_0_419,plain,
lhs_atom138,
c_0_274 ).
fof(c_0_420,plain,
lhs_atom137,
c_0_275 ).
fof(c_0_421,plain,
lhs_atom136,
c_0_276 ).
fof(c_0_422,plain,
lhs_atom135,
c_0_277 ).
fof(c_0_423,plain,
lhs_atom134,
c_0_278 ).
fof(c_0_424,plain,
lhs_atom133,
c_0_279 ).
fof(c_0_425,plain,
lhs_atom132,
c_0_280 ).
fof(c_0_426,plain,
lhs_atom131,
c_0_281 ).
fof(c_0_427,plain,
lhs_atom130,
c_0_282 ).
fof(c_0_428,plain,
lhs_atom129,
c_0_283 ).
fof(c_0_429,plain,
lhs_atom128,
c_0_284 ).
fof(c_0_430,plain,
lhs_atom127,
c_0_285 ).
fof(c_0_431,plain,
lhs_atom126,
c_0_286 ).
fof(c_0_432,plain,
lhs_atom125,
c_0_287 ).
fof(c_0_433,plain,
lhs_atom124,
c_0_288 ).
fof(c_0_434,plain,
lhs_atom16,
c_0_289 ).
cnf(c_0_435,plain,
lhs_atom106(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_436,plain,
lhs_atom105(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_437,plain,
lhs_atom101(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_438,plain,
lhs_atom100(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_439,plain,
lhs_atom39(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_440,plain,
lhs_atom29(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_441,plain,
lhs_atom18(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_442,plain,
lhs_atom10(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_443,plain,
lhs_atom112(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_444,plain,
lhs_atom110(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_445,plain,
lhs_atom76(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_446,plain,
lhs_atom71(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_447,plain,
lhs_atom70(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_448,plain,
lhs_atom66(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_449,plain,
lhs_atom62(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_450,plain,
lhs_atom28(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_451,plain,
lhs_atom27(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_452,plain,
lhs_atom26(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_453,plain,
lhs_atom25(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_454,plain,
lhs_atom8(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_455,plain,
lhs_atom121(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_456,plain,
lhs_atom116(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_457,plain,
lhs_atom115(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_458,plain,
lhs_atom103(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_459,plain,
lhs_atom102(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_460,plain,
lhs_atom96(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_461,plain,
lhs_atom91(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_462,plain,
lhs_atom90(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_463,plain,
lhs_atom89(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_464,plain,
lhs_atom80(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_465,plain,
lhs_atom79(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_466,plain,
lhs_atom78(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_467,plain,
lhs_atom77(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_468,plain,
lhs_atom63(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_469,plain,
lhs_atom57(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_470,plain,
lhs_atom56(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_471,plain,
lhs_atom43(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_472,plain,
lhs_atom37(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_473,plain,
lhs_atom32(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_474,plain,
lhs_atom31(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_475,plain,
lhs_atom23(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_476,plain,
lhs_atom15(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_477,plain,
lhs_atom7(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_478,plain,
lhs_atom3(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_479,plain,
lhs_atom1(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_480,plain,
( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2)
| lhs_atom4(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_481,plain,
lhs_atom123(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_482,plain,
lhs_atom120(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_483,plain,
lhs_atom114(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_484,plain,
lhs_atom99(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_485,plain,
lhs_atom98(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_486,plain,
lhs_atom97(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_487,plain,
lhs_atom55(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_488,plain,
lhs_atom87(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_343]) ).
cnf(c_0_489,plain,
lhs_atom86(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_490,plain,
lhs_atom85(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_491,plain,
lhs_atom84(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_492,plain,
lhs_atom83(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_493,plain,
lhs_atom81(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_494,plain,
lhs_atom75(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_495,plain,
lhs_atom74(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_496,plain,
lhs_atom65(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_351]) ).
cnf(c_0_497,plain,
lhs_atom64(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_498,plain,
lhs_atom61(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_499,plain,
lhs_atom60(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_500,plain,
lhs_atom59(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_501,plain,
lhs_atom55(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_502,plain,
lhs_atom49(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_503,plain,
lhs_atom48(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_504,plain,
lhs_atom47(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_505,plain,
lhs_atom42(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_506,plain,
lhs_atom38(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_507,plain,
lhs_atom36(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_508,plain,
lhs_atom35(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_509,plain,
lhs_atom34(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_510,plain,
lhs_atom33(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_511,plain,
lhs_atom30(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_512,plain,
lhs_atom24(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_513,plain,
lhs_atom19(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_514,plain,
lhs_atom17(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_515,plain,
lhs_atom12(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_516,plain,
lhs_atom9(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_517,plain,
lhs_atom140(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_372]) ).
cnf(c_0_518,plain,
lhs_atom119(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_373]) ).
cnf(c_0_519,plain,
lhs_atom113(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_374]) ).
cnf(c_0_520,plain,
lhs_atom111(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_375]) ).
cnf(c_0_521,plain,
lhs_atom109(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_376]) ).
cnf(c_0_522,plain,
lhs_atom108(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_377]) ).
cnf(c_0_523,plain,
lhs_atom107(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_378]) ).
cnf(c_0_524,plain,
lhs_atom94(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_379]) ).
cnf(c_0_525,plain,
lhs_atom92(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_380]) ).
cnf(c_0_526,plain,
lhs_atom88(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_381]) ).
cnf(c_0_527,plain,
lhs_atom82(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_382]) ).
cnf(c_0_528,plain,
lhs_atom73(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_383]) ).
cnf(c_0_529,plain,
lhs_atom72(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_384]) ).
cnf(c_0_530,plain,
lhs_atom69(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_385]) ).
cnf(c_0_531,plain,
lhs_atom67(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_386]) ).
cnf(c_0_532,plain,
lhs_atom68(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_387]) ).
cnf(c_0_533,plain,
lhs_atom67(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_388]) ).
cnf(c_0_534,plain,
lhs_atom58(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_389]) ).
cnf(c_0_535,plain,
lhs_atom54(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_390]) ).
cnf(c_0_536,plain,
lhs_atom52(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_391]) ).
cnf(c_0_537,plain,
lhs_atom53(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_538,plain,
lhs_atom52(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_539,plain,
lhs_atom51(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_540,plain,
lhs_atom51(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_541,plain,
lhs_atom41(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_542,plain,
lhs_atom40(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_543,plain,
lhs_atom21(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_544,plain,
lhs_atom21(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_399]) ).
cnf(c_0_545,plain,
lhs_atom20(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_546,plain,
lhs_atom122(X1),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_547,plain,
lhs_atom118(X1),
inference(split_conjunct,[status(thm)],[c_0_402]) ).
cnf(c_0_548,plain,
lhs_atom117(X1),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_549,plain,
lhs_atom104(X1),
inference(split_conjunct,[status(thm)],[c_0_404]) ).
cnf(c_0_550,plain,
lhs_atom95(X1),
inference(split_conjunct,[status(thm)],[c_0_405]) ).
cnf(c_0_551,plain,
lhs_atom93(X1),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_552,plain,
lhs_atom50(X1),
inference(split_conjunct,[status(thm)],[c_0_407]) ).
cnf(c_0_553,plain,
lhs_atom46(X1),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_554,plain,
lhs_atom45(X1),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_555,plain,
lhs_atom44(X1),
inference(split_conjunct,[status(thm)],[c_0_410]) ).
cnf(c_0_556,plain,
lhs_atom22(X1),
inference(split_conjunct,[status(thm)],[c_0_411]) ).
cnf(c_0_557,plain,
lhs_atom14(X1),
inference(split_conjunct,[status(thm)],[c_0_412]) ).
cnf(c_0_558,plain,
lhs_atom13(X1),
inference(split_conjunct,[status(thm)],[c_0_413]) ).
cnf(c_0_559,plain,
lhs_atom11(X1),
inference(split_conjunct,[status(thm)],[c_0_414]) ).
cnf(c_0_560,plain,
lhs_atom6(X1),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_561,plain,
lhs_atom5(X1),
inference(split_conjunct,[status(thm)],[c_0_416]) ).
cnf(c_0_562,plain,
lhs_atom2(X1),
inference(split_conjunct,[status(thm)],[c_0_417]) ).
cnf(c_0_563,plain,
lhs_atom139,
inference(split_conjunct,[status(thm)],[c_0_418]) ).
cnf(c_0_564,plain,
lhs_atom138,
inference(split_conjunct,[status(thm)],[c_0_419]) ).
cnf(c_0_565,plain,
lhs_atom137,
inference(split_conjunct,[status(thm)],[c_0_420]) ).
cnf(c_0_566,plain,
lhs_atom136,
inference(split_conjunct,[status(thm)],[c_0_421]) ).
cnf(c_0_567,plain,
lhs_atom135,
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_568,plain,
lhs_atom134,
inference(split_conjunct,[status(thm)],[c_0_423]) ).
cnf(c_0_569,plain,
lhs_atom133,
inference(split_conjunct,[status(thm)],[c_0_424]) ).
cnf(c_0_570,plain,
lhs_atom132,
inference(split_conjunct,[status(thm)],[c_0_425]) ).
cnf(c_0_571,plain,
lhs_atom131,
inference(split_conjunct,[status(thm)],[c_0_426]) ).
cnf(c_0_572,plain,
lhs_atom130,
inference(split_conjunct,[status(thm)],[c_0_427]) ).
cnf(c_0_573,plain,
lhs_atom129,
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_574,plain,
lhs_atom128,
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_575,plain,
lhs_atom127,
inference(split_conjunct,[status(thm)],[c_0_430]) ).
cnf(c_0_576,plain,
lhs_atom126,
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_577,plain,
lhs_atom125,
inference(split_conjunct,[status(thm)],[c_0_432]) ).
cnf(c_0_578,plain,
lhs_atom124,
inference(split_conjunct,[status(thm)],[c_0_433]) ).
cnf(c_0_579,plain,
lhs_atom16,
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_580,plain,
lhs_atom106(X1,X2,X3,X4,X5,X6),
c_0_435,
[final] ).
cnf(c_0_581,plain,
lhs_atom105(X1,X2,X3,X4,X5,X6),
c_0_436,
[final] ).
cnf(c_0_582,plain,
lhs_atom101(X1,X2,X3,X4,X5,X6),
c_0_437,
[final] ).
cnf(c_0_583,plain,
lhs_atom100(X1,X2,X3,X4,X5,X6),
c_0_438,
[final] ).
cnf(c_0_584,plain,
lhs_atom39(X1,X2,X3,X4,X5,X6),
c_0_439,
[final] ).
cnf(c_0_585,plain,
lhs_atom29(X1,X2,X3,X4,X5,X6),
c_0_440,
[final] ).
cnf(c_0_586,plain,
lhs_atom18(X1,X2,X3,X4,X5,X6),
c_0_441,
[final] ).
cnf(c_0_587,plain,
lhs_atom10(X1,X2,X3,X4,X5,X6),
c_0_442,
[final] ).
cnf(c_0_588,plain,
lhs_atom112(X1,X2,X3,X4,X5),
c_0_443,
[final] ).
cnf(c_0_589,plain,
lhs_atom110(X1,X2,X3,X4,X5),
c_0_444,
[final] ).
cnf(c_0_590,plain,
lhs_atom76(X1,X2,X3,X4,X5),
c_0_445,
[final] ).
cnf(c_0_591,plain,
lhs_atom71(X1,X2,X3,X4,X5),
c_0_446,
[final] ).
cnf(c_0_592,plain,
lhs_atom70(X1,X2,X3,X4,X5),
c_0_447,
[final] ).
cnf(c_0_593,plain,
lhs_atom66(X1,X2,X3,X4,X5),
c_0_448,
[final] ).
cnf(c_0_594,plain,
lhs_atom62(X1,X2,X3,X4,X5),
c_0_449,
[final] ).
cnf(c_0_595,plain,
lhs_atom28(X1,X2,X3,X4,X5),
c_0_450,
[final] ).
cnf(c_0_596,plain,
lhs_atom27(X1,X2,X3,X4,X5),
c_0_451,
[final] ).
cnf(c_0_597,plain,
lhs_atom26(X1,X2,X3,X4,X5),
c_0_452,
[final] ).
cnf(c_0_598,plain,
lhs_atom25(X1,X2,X3,X4,X5),
c_0_453,
[final] ).
cnf(c_0_599,plain,
lhs_atom8(X1,X2,X3,X4,X5),
c_0_454,
[final] ).
cnf(c_0_600,plain,
lhs_atom121(X1,X2,X3,X4),
c_0_455,
[final] ).
cnf(c_0_601,plain,
lhs_atom116(X1,X2,X3,X4),
c_0_456,
[final] ).
cnf(c_0_602,plain,
lhs_atom115(X1,X2,X3,X4),
c_0_457,
[final] ).
cnf(c_0_603,plain,
lhs_atom103(X1,X2,X3,X4),
c_0_458,
[final] ).
cnf(c_0_604,plain,
lhs_atom102(X1,X2,X3,X4),
c_0_459,
[final] ).
cnf(c_0_605,plain,
lhs_atom96(X1,X2,X3,X4),
c_0_460,
[final] ).
cnf(c_0_606,plain,
lhs_atom91(X1,X2,X3,X4),
c_0_461,
[final] ).
cnf(c_0_607,plain,
lhs_atom90(X1,X2,X3,X4),
c_0_462,
[final] ).
cnf(c_0_608,plain,
lhs_atom89(X1,X2,X3,X4),
c_0_463,
[final] ).
cnf(c_0_609,plain,
lhs_atom80(X1,X2,X3,X4),
c_0_464,
[final] ).
cnf(c_0_610,plain,
lhs_atom79(X1,X2,X3,X4),
c_0_465,
[final] ).
cnf(c_0_611,plain,
lhs_atom78(X1,X2,X3,X4),
c_0_466,
[final] ).
cnf(c_0_612,plain,
lhs_atom77(X1,X2,X3,X4),
c_0_467,
[final] ).
cnf(c_0_613,plain,
lhs_atom63(X1,X2,X3,X4),
c_0_468,
[final] ).
cnf(c_0_614,plain,
lhs_atom57(X1,X2,X3,X4),
c_0_469,
[final] ).
cnf(c_0_615,plain,
lhs_atom56(X1,X2,X3,X4),
c_0_470,
[final] ).
cnf(c_0_616,plain,
lhs_atom43(X1,X2,X3,X4),
c_0_471,
[final] ).
cnf(c_0_617,plain,
lhs_atom37(X1,X2,X3,X4),
c_0_472,
[final] ).
cnf(c_0_618,plain,
lhs_atom32(X1,X2,X3,X4),
c_0_473,
[final] ).
cnf(c_0_619,plain,
lhs_atom31(X1,X2,X3,X4),
c_0_474,
[final] ).
cnf(c_0_620,plain,
lhs_atom23(X1,X2,X3,X4),
c_0_475,
[final] ).
cnf(c_0_621,plain,
lhs_atom15(X1,X2,X3,X4),
c_0_476,
[final] ).
cnf(c_0_622,plain,
lhs_atom7(X1,X2,X3,X4),
c_0_477,
[final] ).
cnf(c_0_623,plain,
lhs_atom3(X1,X2,X3,X4),
c_0_478,
[final] ).
cnf(c_0_624,plain,
lhs_atom1(X1,X2,X3,X4),
c_0_479,
[final] ).
cnf(c_0_625,plain,
( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2)
| lhs_atom4(X3,X1,X2) ),
c_0_480,
[final] ).
cnf(c_0_626,plain,
lhs_atom123(X1,X2,X3),
c_0_481,
[final] ).
cnf(c_0_627,plain,
lhs_atom120(X1,X2,X3),
c_0_482,
[final] ).
cnf(c_0_628,plain,
lhs_atom114(X1,X2,X3),
c_0_483,
[final] ).
cnf(c_0_629,plain,
lhs_atom99(X1,X2,X3),
c_0_484,
[final] ).
cnf(c_0_630,plain,
lhs_atom98(X1,X2,X3),
c_0_485,
[final] ).
cnf(c_0_631,plain,
lhs_atom97(X1,X2,X3),
c_0_486,
[final] ).
cnf(c_0_632,plain,
lhs_atom55(X1,X2,X3),
c_0_487,
[final] ).
cnf(c_0_633,plain,
lhs_atom87(X1,X2,X3),
c_0_488,
[final] ).
cnf(c_0_634,plain,
lhs_atom86(X1,X2,X3),
c_0_489,
[final] ).
cnf(c_0_635,plain,
lhs_atom85(X1,X2,X3),
c_0_490,
[final] ).
cnf(c_0_636,plain,
lhs_atom84(X1,X2,X3),
c_0_491,
[final] ).
cnf(c_0_637,plain,
lhs_atom83(X1,X2,X3),
c_0_492,
[final] ).
cnf(c_0_638,plain,
lhs_atom81(X1,X2,X3),
c_0_493,
[final] ).
cnf(c_0_639,plain,
lhs_atom75(X1,X2,X3),
c_0_494,
[final] ).
cnf(c_0_640,plain,
lhs_atom74(X1,X2,X3),
c_0_495,
[final] ).
cnf(c_0_641,plain,
lhs_atom65(X1,X2,X3),
c_0_496,
[final] ).
cnf(c_0_642,plain,
lhs_atom64(X1,X2,X3),
c_0_497,
[final] ).
cnf(c_0_643,plain,
lhs_atom61(X1,X2,X3),
c_0_498,
[final] ).
cnf(c_0_644,plain,
lhs_atom60(X1,X2,X3),
c_0_499,
[final] ).
cnf(c_0_645,plain,
lhs_atom59(X1,X2,X3),
c_0_500,
[final] ).
cnf(c_0_646,plain,
lhs_atom55(X1,X2,X3),
c_0_501,
[final] ).
cnf(c_0_647,plain,
lhs_atom49(X1,X2,X3),
c_0_502,
[final] ).
cnf(c_0_648,plain,
lhs_atom48(X1,X2,X3),
c_0_503,
[final] ).
cnf(c_0_649,plain,
lhs_atom47(X1,X2,X3),
c_0_504,
[final] ).
cnf(c_0_650,plain,
lhs_atom42(X1,X2,X3),
c_0_505,
[final] ).
cnf(c_0_651,plain,
lhs_atom38(X1,X2,X3),
c_0_506,
[final] ).
cnf(c_0_652,plain,
lhs_atom36(X1,X2,X3),
c_0_507,
[final] ).
cnf(c_0_653,plain,
lhs_atom35(X1,X2,X3),
c_0_508,
[final] ).
cnf(c_0_654,plain,
lhs_atom34(X1,X2,X3),
c_0_509,
[final] ).
cnf(c_0_655,plain,
lhs_atom33(X1,X2,X3),
c_0_510,
[final] ).
cnf(c_0_656,plain,
lhs_atom30(X1,X2,X3),
c_0_511,
[final] ).
cnf(c_0_657,plain,
lhs_atom24(X1,X2,X3),
c_0_512,
[final] ).
cnf(c_0_658,plain,
lhs_atom19(X1,X2,X3),
c_0_513,
[final] ).
cnf(c_0_659,plain,
lhs_atom17(X1,X2,X3),
c_0_514,
[final] ).
cnf(c_0_660,plain,
lhs_atom12(X1,X2,X3),
c_0_515,
[final] ).
cnf(c_0_661,plain,
lhs_atom9(X1,X2,X3),
c_0_516,
[final] ).
cnf(c_0_662,plain,
lhs_atom140(X1,X2),
c_0_517,
[final] ).
cnf(c_0_663,plain,
lhs_atom119(X1,X2),
c_0_518,
[final] ).
cnf(c_0_664,plain,
lhs_atom113(X1,X2),
c_0_519,
[final] ).
cnf(c_0_665,plain,
lhs_atom111(X1,X2),
c_0_520,
[final] ).
cnf(c_0_666,plain,
lhs_atom109(X1,X2),
c_0_521,
[final] ).
cnf(c_0_667,plain,
lhs_atom108(X1,X2),
c_0_522,
[final] ).
cnf(c_0_668,plain,
lhs_atom107(X1,X2),
c_0_523,
[final] ).
cnf(c_0_669,plain,
lhs_atom94(X1,X2),
c_0_524,
[final] ).
cnf(c_0_670,plain,
lhs_atom92(X1,X2),
c_0_525,
[final] ).
cnf(c_0_671,plain,
lhs_atom88(X1,X2),
c_0_526,
[final] ).
cnf(c_0_672,plain,
lhs_atom82(X1,X2),
c_0_527,
[final] ).
cnf(c_0_673,plain,
lhs_atom73(X1,X2),
c_0_528,
[final] ).
cnf(c_0_674,plain,
lhs_atom72(X1,X2),
c_0_529,
[final] ).
cnf(c_0_675,plain,
lhs_atom69(X1,X2),
c_0_530,
[final] ).
cnf(c_0_676,plain,
lhs_atom67(X1,X2),
c_0_531,
[final] ).
cnf(c_0_677,plain,
lhs_atom68(X1,X2),
c_0_532,
[final] ).
cnf(c_0_678,plain,
lhs_atom67(X1,X2),
c_0_533,
[final] ).
cnf(c_0_679,plain,
lhs_atom58(X1,X2),
c_0_534,
[final] ).
cnf(c_0_680,plain,
lhs_atom54(X1,X2),
c_0_535,
[final] ).
cnf(c_0_681,plain,
lhs_atom52(X1,X2),
c_0_536,
[final] ).
cnf(c_0_682,plain,
lhs_atom53(X1,X2),
c_0_537,
[final] ).
cnf(c_0_683,plain,
lhs_atom52(X1,X2),
c_0_538,
[final] ).
cnf(c_0_684,plain,
lhs_atom51(X1,X2),
c_0_539,
[final] ).
cnf(c_0_685,plain,
lhs_atom51(X1,X2),
c_0_540,
[final] ).
cnf(c_0_686,plain,
lhs_atom41(X1,X2),
c_0_541,
[final] ).
cnf(c_0_687,plain,
lhs_atom40(X1,X2),
c_0_542,
[final] ).
cnf(c_0_688,plain,
lhs_atom21(X1,X2),
c_0_543,
[final] ).
cnf(c_0_689,plain,
lhs_atom21(X1,X2),
c_0_544,
[final] ).
cnf(c_0_690,plain,
lhs_atom20(X1,X2),
c_0_545,
[final] ).
cnf(c_0_691,plain,
lhs_atom122(X1),
c_0_546,
[final] ).
cnf(c_0_692,plain,
lhs_atom118(X1),
c_0_547,
[final] ).
cnf(c_0_693,plain,
lhs_atom117(X1),
c_0_548,
[final] ).
cnf(c_0_694,plain,
lhs_atom104(X1),
c_0_549,
[final] ).
cnf(c_0_695,plain,
lhs_atom95(X1),
c_0_550,
[final] ).
cnf(c_0_696,plain,
lhs_atom93(X1),
c_0_551,
[final] ).
cnf(c_0_697,plain,
lhs_atom50(X1),
c_0_552,
[final] ).
cnf(c_0_698,plain,
lhs_atom46(X1),
c_0_553,
[final] ).
cnf(c_0_699,plain,
lhs_atom45(X1),
c_0_554,
[final] ).
cnf(c_0_700,plain,
lhs_atom44(X1),
c_0_555,
[final] ).
cnf(c_0_701,plain,
lhs_atom22(X1),
c_0_556,
[final] ).
cnf(c_0_702,plain,
lhs_atom14(X1),
c_0_557,
[final] ).
cnf(c_0_703,plain,
lhs_atom13(X1),
c_0_558,
[final] ).
cnf(c_0_704,plain,
lhs_atom11(X1),
c_0_559,
[final] ).
cnf(c_0_705,plain,
lhs_atom6(X1),
c_0_560,
[final] ).
cnf(c_0_706,plain,
lhs_atom5(X1),
c_0_561,
[final] ).
cnf(c_0_707,plain,
lhs_atom2(X1),
c_0_562,
[final] ).
cnf(c_0_708,plain,
lhs_atom139,
c_0_563,
[final] ).
cnf(c_0_709,plain,
lhs_atom138,
c_0_564,
[final] ).
cnf(c_0_710,plain,
lhs_atom137,
c_0_565,
[final] ).
cnf(c_0_711,plain,
lhs_atom136,
c_0_566,
[final] ).
cnf(c_0_712,plain,
lhs_atom135,
c_0_567,
[final] ).
cnf(c_0_713,plain,
lhs_atom134,
c_0_568,
[final] ).
cnf(c_0_714,plain,
lhs_atom133,
c_0_569,
[final] ).
cnf(c_0_715,plain,
lhs_atom132,
c_0_570,
[final] ).
cnf(c_0_716,plain,
lhs_atom131,
c_0_571,
[final] ).
cnf(c_0_717,plain,
lhs_atom130,
c_0_572,
[final] ).
cnf(c_0_718,plain,
lhs_atom129,
c_0_573,
[final] ).
cnf(c_0_719,plain,
lhs_atom128,
c_0_574,
[final] ).
cnf(c_0_720,plain,
lhs_atom127,
c_0_575,
[final] ).
cnf(c_0_721,plain,
lhs_atom126,
c_0_576,
[final] ).
cnf(c_0_722,plain,
lhs_atom125,
c_0_577,
[final] ).
cnf(c_0_723,plain,
lhs_atom124,
c_0_578,
[final] ).
cnf(c_0_724,plain,
lhs_atom16,
c_0_579,
[final] ).
% End CNF derivation
cnf(c_0_625_0,axiom,
( c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2)
| c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_625,def_lhs_atom4]) ).
cnf(c_0_580_0,axiom,
c_List_Ofoldl(X3,X4,c_List_Oappend(X2,X1,X5),X6,X5) = c_List_Ofoldl(X3,c_List_Ofoldl(X3,X4,X2,X6,X5),X1,X6,X5),
inference(unfold_definition,[status(thm)],[c_0_580,def_lhs_atom106]) ).
cnf(c_0_581_0,axiom,
c_List_Ofoldl(X3,X4,c_List_Olist_OCons(X2,X1,X5),X6,X5) = c_List_Ofoldl(X3,hAPP(hAPP(X3,X4),X2),X1,X6,X5),
inference(unfold_definition,[status(thm)],[c_0_581,def_lhs_atom105]) ).
cnf(c_0_582_0,axiom,
c_Lambda_OdB_OdB__rec(X3,X2,X1,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X4),X6) = hAPP(hAPP(hAPP(hAPP(X2,X5),X4),c_Lambda_OdB_OdB__rec(X3,X2,X1,X5,X6)),c_Lambda_OdB_OdB__rec(X3,X2,X1,X4,X6)),
inference(unfold_definition,[status(thm)],[c_0_582,def_lhs_atom101]) ).
cnf(c_0_583_0,axiom,
c_Lambda_OdB_OdB__case(X3,X2,X1,hAPP(hAPP(c_Lambda_OdB_OApp,X5),X4),X6) = hAPP(hAPP(X2,X5),X4),
inference(unfold_definition,[status(thm)],[c_0_583,def_lhs_atom100]) ).
cnf(c_0_584_0,axiom,
c_List_Omap(X4,c_List_Olist__update(X2,X3,X1,X5),X5,X6) = c_List_Olist__update(c_List_Omap(X4,X2,X5,X6),X3,hAPP(X4,X1),X6),
inference(unfold_definition,[status(thm)],[c_0_584,def_lhs_atom39]) ).
cnf(c_0_585_0,axiom,
c_List_Olist_Olist__case(X3,X2,c_List_Olist_OCons(X4,X1,X5),X6,X5) = hAPP(hAPP(X2,X4),X1),
inference(unfold_definition,[status(thm)],[c_0_585,def_lhs_atom29]) ).
cnf(c_0_586_0,axiom,
c_List_Ofoldr(X3,c_List_Olist_OCons(X2,X1,X5),X4,X5,X6) = hAPP(hAPP(X3,X2),c_List_Ofoldr(X3,X1,X4,X5,X6)),
inference(unfold_definition,[status(thm)],[c_0_586,def_lhs_atom18]) ).
cnf(c_0_587_0,axiom,
c_List_Ofoldr(X3,c_List_Oappend(X2,X1,X5),X4,X5,X6) = c_List_Ofoldr(X3,X2,c_List_Ofoldr(X3,X1,X4,X5,X6),X5,X6),
inference(unfold_definition,[status(thm)],[c_0_587,def_lhs_atom10]) ).
cnf(c_0_588_0,axiom,
c_Lambda_OdB_OdB__case(X4,X3,X2,c_Lambda_OdB_OVar(X1),X5) = hAPP(X4,X1),
inference(unfold_definition,[status(thm)],[c_0_588,def_lhs_atom112]) ).
cnf(c_0_589_0,axiom,
c_Lambda_OdB_OdB__rec(X4,X3,X2,c_Lambda_OdB_OVar(X1),X5) = hAPP(X4,X1),
inference(unfold_definition,[status(thm)],[c_0_589,def_lhs_atom110]) ).
cnf(c_0_590_0,axiom,
c_List_Olist__update(c_List_Olist__update(X2,X4,X3,X5),X4,X1,X5) = c_List_Olist__update(X2,X4,X1,X5),
inference(unfold_definition,[status(thm)],[c_0_590,def_lhs_atom76]) ).
cnf(c_0_591_0,axiom,
c_Lambda_OdB_OdB__rec(X3,X2,X1,c_Lambda_OdB_OAbs(X4),X5) = hAPP(hAPP(X1,X4),c_Lambda_OdB_OdB__rec(X3,X2,X1,X4,X5)),
inference(unfold_definition,[status(thm)],[c_0_591,def_lhs_atom71]) ).
cnf(c_0_592_0,axiom,
c_List_Omap(X3,c_List_Oappend(X2,X1,X4),X4,X5) = c_List_Oappend(c_List_Omap(X3,X2,X4,X5),c_List_Omap(X3,X1,X4,X5),X5),
inference(unfold_definition,[status(thm)],[c_0_592,def_lhs_atom70]) ).
cnf(c_0_593_0,axiom,
c_List_Orotate(X2,c_List_Omap(X3,X1,X4,X5),X5) = c_List_Omap(X3,c_List_Orotate(X2,X1,X4),X4,X5),
inference(unfold_definition,[status(thm)],[c_0_593,def_lhs_atom66]) ).
cnf(c_0_594_0,axiom,
c_Lambda_OdB_OdB__case(X3,X2,X1,c_Lambda_OdB_OAbs(X4),X5) = hAPP(X1,X4),
inference(unfold_definition,[status(thm)],[c_0_594,def_lhs_atom62]) ).
cnf(c_0_595_0,axiom,
c_List_Omap(X3,c_List_Olist_OCons(X2,X1,X4),X4,X5) = c_List_Olist_OCons(hAPP(X3,X2),c_List_Omap(X3,X1,X4,X5),X5),
inference(unfold_definition,[status(thm)],[c_0_595,def_lhs_atom28]) ).
cnf(c_0_596_0,axiom,
c_List_Olist_OCons(hAPP(X3,X2),c_List_Omap(X3,X1,X4,X5),X5) = c_List_Omap(X3,c_List_Olist_OCons(X2,X1,X4),X4,X5),
inference(unfold_definition,[status(thm)],[c_0_596,def_lhs_atom27]) ).
cnf(c_0_597_0,axiom,
c_List_Omap(X3,c_List_Olist_OCons(X2,X1,X4),X4,X5) = c_List_Olist_OCons(hAPP(X3,X2),c_List_Omap(X3,X1,X4,X5),X5),
inference(unfold_definition,[status(thm)],[c_0_597,def_lhs_atom26]) ).
cnf(c_0_598_0,axiom,
c_List_Olist__update(c_List_Oappend(X3,c_List_Olist_OCons(X4,X1,X5),X5),c_Nat_Osize__class_Osize(X3,tc_List_Olist(X5)),X2,X5) = c_List_Oappend(X3,c_List_Olist_OCons(X2,X1,X5),X5),
inference(unfold_definition,[status(thm)],[c_0_598,def_lhs_atom25]) ).
cnf(c_0_599_0,axiom,
c_List_Omap(X3,c_List_Oreplicate(X2,X1,X4),X4,X5) = c_List_Oreplicate(X2,hAPP(X3,X1),X5),
inference(unfold_definition,[status(thm)],[c_0_599,def_lhs_atom8]) ).
cnf(c_0_600_0,axiom,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
inference(unfold_definition,[status(thm)],[c_0_600,def_lhs_atom121]) ).
cnf(c_0_601_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3)),X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_601,def_lhs_atom116]) ).
cnf(c_0_602_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X2,tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_602,def_lhs_atom115]) ).
cnf(c_0_603_0,axiom,
c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X2,X3,X4)),c_Lambda_Osubstn(X1,X3,X4)),
inference(unfold_definition,[status(thm)],[c_0_603,def_lhs_atom103]) ).
cnf(c_0_604_0,axiom,
c_Lambda_Oliftn(X3,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X3,X2,X4)),c_Lambda_Oliftn(X3,X1,X4)),
inference(unfold_definition,[status(thm)],[c_0_604,def_lhs_atom102]) ).
cnf(c_0_605_0,axiom,
c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X2,X3,X4)),c_Lambda_Osubst(X1,X3,X4)),
inference(unfold_definition,[status(thm)],[c_0_605,def_lhs_atom96]) ).
cnf(c_0_606_0,axiom,
c_List_Olist_Olist__case(X2,X1,c_List_Olist_ONil(X3),X4,X3) = X2,
inference(unfold_definition,[status(thm)],[c_0_606,def_lhs_atom91]) ).
cnf(c_0_607_0,axiom,
c_Map_Omap__upds(X1,c_List_Olist_ONil(X4),X2,X4,X3) = X1,
inference(unfold_definition,[status(thm)],[c_0_607,def_lhs_atom90]) ).
cnf(c_0_608_0,axiom,
c_Map_Omap__upds(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X1,
inference(unfold_definition,[status(thm)],[c_0_608,def_lhs_atom89]) ).
cnf(c_0_609_0,axiom,
c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4),
inference(unfold_definition,[status(thm)],[c_0_609,def_lhs_atom80]) ).
cnf(c_0_610_0,axiom,
c_List_Oappend(c_List_Oappend(X1,X3,X4),X2,X4) = c_List_Oappend(X1,c_List_Oappend(X3,X2,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_610,def_lhs_atom79]) ).
cnf(c_0_611_0,axiom,
c_List_Oappend(X2,c_List_Oappend(X1,X3,X4),X4) = c_List_Oappend(c_List_Oappend(X2,X1,X4),X3,X4),
inference(unfold_definition,[status(thm)],[c_0_611,def_lhs_atom78]) ).
cnf(c_0_612_0,axiom,
c_List_Oappend(c_List_Oappend(X3,X2,X4),X1,X4) = c_List_Oappend(X3,c_List_Oappend(X2,X1,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_612,def_lhs_atom77]) ).
cnf(c_0_613_0,axiom,
c_List_Orev(c_List_Omap(X2,X1,X3,X4),X4) = c_List_Omap(X2,c_List_Orev(X1,X3),X3,X4),
inference(unfold_definition,[status(thm)],[c_0_613,def_lhs_atom63]) ).
cnf(c_0_614_0,axiom,
c_List_Oappend(c_List_Olist_OCons(X3,X2,X4),X1,X4) = c_List_Olist_OCons(X3,c_List_Oappend(X2,X1,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_614,def_lhs_atom57]) ).
cnf(c_0_615_0,axiom,
c_List_Oappend(c_List_Olist_OCons(X3,X2,X4),X1,X4) = c_List_Olist_OCons(X3,c_List_Oappend(X2,X1,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_615,def_lhs_atom56]) ).
cnf(c_0_616_0,axiom,
c_List_Ofilter(X3,c_List_Oappend(X2,X1,X4),X4) = c_List_Oappend(c_List_Ofilter(X3,X2,X4),c_List_Ofilter(X3,X1,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_616,def_lhs_atom43]) ).
cnf(c_0_617_0,axiom,
c_List_Olist__update(c_List_Olist_OCons(X3,X2,X4),c_HOL_Ozero__class_Ozero(tc_nat),X1,X4) = c_List_Olist_OCons(X1,X2,X4),
inference(unfold_definition,[status(thm)],[c_0_617,def_lhs_atom37]) ).
cnf(c_0_618_0,axiom,
c_List_Olist_OCons(X3,c_List_Oappend(X2,X1,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X3,X2,X4),X1,X4),
inference(unfold_definition,[status(thm)],[c_0_618,def_lhs_atom32]) ).
cnf(c_0_619_0,axiom,
c_List_Olist_OCons(X3,c_List_Oappend(X2,X1,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X3,X2,X4),X1,X4),
inference(unfold_definition,[status(thm)],[c_0_619,def_lhs_atom31]) ).
cnf(c_0_620_0,axiom,
c_List_Oappend(c_List_Oreplicate(X3,X2,X4),c_List_Olist_OCons(X2,X1,X4),X4) = c_List_Olist_OCons(X2,c_List_Oappend(c_List_Oreplicate(X3,X2,X4),X1,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_620,def_lhs_atom23]) ).
cnf(c_0_621_0,axiom,
c_List_Oappend(c_List_Oreplicate(X2,X1,X4),c_List_Oreplicate(X3,X1,X4),X4) = c_List_Oappend(c_List_Oreplicate(X3,X1,X4),c_List_Oreplicate(X2,X1,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_621,def_lhs_atom15]) ).
cnf(c_0_622_0,axiom,
c_Nat_Osize__class_Osize(c_List_Omap(X2,X1,X3,X4),tc_List_Olist(X4)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),
inference(unfold_definition,[status(thm)],[c_0_622,def_lhs_atom7]) ).
cnf(c_0_623_0,axiom,
c_Nat_Osize__class_Osize(c_List_Olist__update(X1,X3,X2,X4),tc_List_Olist(X4)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X4)),
inference(unfold_definition,[status(thm)],[c_0_623,def_lhs_atom3]) ).
cnf(c_0_624_0,axiom,
c_List_Ofoldr(X1,c_List_Olist_ONil(X3),X2,X3,X4) = X2,
inference(unfold_definition,[status(thm)],[c_0_624,def_lhs_atom1]) ).
cnf(c_0_626_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2) != c_Lambda_OdB_OVar(X1),
inference(unfold_definition,[status(thm)],[c_0_626,def_lhs_atom123]) ).
cnf(c_0_627_0,axiom,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2),
inference(unfold_definition,[status(thm)],[c_0_627,def_lhs_atom120]) ).
cnf(c_0_628_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Oappend(X2,c_List_Olist_OCons(X1,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_628,def_lhs_atom114]) ).
cnf(c_0_629_0,axiom,
c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X2,X3)),c_Lambda_Olift(X1,X3)),
inference(unfold_definition,[status(thm)],[c_0_629,def_lhs_atom99]) ).
cnf(c_0_630_0,axiom,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2),
inference(unfold_definition,[status(thm)],[c_0_630,def_lhs_atom98]) ).
cnf(c_0_631_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2) != c_Lambda_OdB_OAbs(X1),
inference(unfold_definition,[status(thm)],[c_0_631,def_lhs_atom97]) ).
cnf(c_0_632_0,axiom,
c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
inference(unfold_definition,[status(thm)],[c_0_632,def_lhs_atom55]) ).
cnf(c_0_633_0,axiom,
c_List_Olist_OCons(X2,X1,X3) != c_List_Olist_ONil(X3),
inference(unfold_definition,[status(thm)],[c_0_633,def_lhs_atom87]) ).
cnf(c_0_634_0,axiom,
c_List_Olist_OCons(X2,X1,X3) != c_List_Olist_ONil(X3),
inference(unfold_definition,[status(thm)],[c_0_634,def_lhs_atom86]) ).
cnf(c_0_635_0,axiom,
c_List_Olist__update(c_List_Olist_ONil(X3),X2,X1,X3) = c_List_Olist_ONil(X3),
inference(unfold_definition,[status(thm)],[c_0_635,def_lhs_atom85]) ).
cnf(c_0_636_0,axiom,
c_List_Olist__update(c_List_Olist_ONil(X3),X2,X1,X3) = c_List_Olist_ONil(X3),
inference(unfold_definition,[status(thm)],[c_0_636,def_lhs_atom84]) ).
cnf(c_0_637_0,axiom,
c_List_Olist__update(c_List_Olist_ONil(X3),X2,X1,X3) = c_List_Olist_ONil(X3),
inference(unfold_definition,[status(thm)],[c_0_637,def_lhs_atom83]) ).
cnf(c_0_638_0,axiom,
c_List_Ofiltermap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
inference(unfold_definition,[status(thm)],[c_0_638,def_lhs_atom81]) ).
cnf(c_0_639_0,axiom,
c_List_Orev(c_List_Ofilter(X2,X1,X3),X3) = c_List_Ofilter(X2,c_List_Orev(X1,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_639,def_lhs_atom75]) ).
cnf(c_0_640_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X3),c_List_Olist_OCons(X2,X1,X3),X3) = c_List_Olist_OCons(X2,X1,X3),
inference(unfold_definition,[status(thm)],[c_0_640,def_lhs_atom74]) ).
cnf(c_0_641_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X2,X3),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_641,def_lhs_atom65]) ).
cnf(c_0_642_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X2),X2)),
inference(unfold_definition,[status(thm)],[c_0_642,def_lhs_atom64]) ).
cnf(c_0_643_0,axiom,
c_Lambda_Osubstn(X1,X2,X3) = c_Lambda_Osubst(X1,c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3),
inference(unfold_definition,[status(thm)],[c_0_643,def_lhs_atom61]) ).
cnf(c_0_644_0,axiom,
c_List_Oremdups(c_List_Ofilter(X2,X1,X3),X3) = c_List_Ofilter(X2,c_List_Oremdups(X1,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_644,def_lhs_atom60]) ).
cnf(c_0_645_0,axiom,
c_List_Orev(c_List_Olist_OCons(X2,X1,X3),X3) = c_List_Oappend(c_List_Orev(X1,X3),c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3),
inference(unfold_definition,[status(thm)],[c_0_645,def_lhs_atom59]) ).
cnf(c_0_646_0,axiom,
c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3) = c_List_Olist_ONil(X3),
inference(unfold_definition,[status(thm)],[c_0_646,def_lhs_atom55]) ).
cnf(c_0_647_0,axiom,
~ c_ListOrder_Ostep1(X2,c_List_Olist_ONil(X3),X1,X3),
inference(unfold_definition,[status(thm)],[c_0_647,def_lhs_atom49]) ).
cnf(c_0_648_0,axiom,
~ c_ListOrder_Ostep1(X2,X1,c_List_Olist_ONil(X3),X3),
inference(unfold_definition,[status(thm)],[c_0_648,def_lhs_atom48]) ).
cnf(c_0_649_0,axiom,
c_List_Olist_ONil(X3) != c_List_Olist_OCons(X2,X1,X3),
inference(unfold_definition,[status(thm)],[c_0_649,def_lhs_atom47]) ).
cnf(c_0_650_0,axiom,
c_List_Orev(c_List_Oappend(X2,X1,X3),X3) = c_List_Oappend(c_List_Orev(X1,X3),c_List_Orev(X2,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_650,def_lhs_atom42]) ).
cnf(c_0_651_0,axiom,
c_List_Olist_OCons(X2,X1,X3) = c_List_Oappend(c_List_Olist_ONil(X3),c_List_Olist_OCons(X2,X1,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_651,def_lhs_atom38]) ).
cnf(c_0_652_0,axiom,
X1 != c_List_Olist_OCons(X2,X1,X3),
inference(unfold_definition,[status(thm)],[c_0_652,def_lhs_atom36]) ).
cnf(c_0_653_0,axiom,
c_List_Olist_OCons(X1,X2,X3) != X2,
inference(unfold_definition,[status(thm)],[c_0_653,def_lhs_atom35]) ).
cnf(c_0_654_0,axiom,
c_Lambda_Osubst(c_Lambda_Olift(X1,X3),X2,X3) = X1,
inference(unfold_definition,[status(thm)],[c_0_654,def_lhs_atom34]) ).
cnf(c_0_655_0,axiom,
c_List_Orev(c_List_Oappend(c_List_Orev(X1,X3),c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3),X3) = c_List_Olist_OCons(X2,X1,X3),
inference(unfold_definition,[status(thm)],[c_0_655,def_lhs_atom33]) ).
cnf(c_0_656_0,axiom,
c_List_Oremove1(X2,c_List_Olist_OCons(X2,X1,X3),X3) = X1,
inference(unfold_definition,[status(thm)],[c_0_656,def_lhs_atom30]) ).
cnf(c_0_657_0,axiom,
c_List_Oappend(c_List_Oreplicate(X2,X1,X3),c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3) = c_List_Olist_OCons(X1,c_List_Oreplicate(X2,X1,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_657,def_lhs_atom24]) ).
cnf(c_0_658_0,axiom,
c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X3,X2),X2,X3) = X1,
inference(unfold_definition,[status(thm)],[c_0_658,def_lhs_atom19]) ).
cnf(c_0_659_0,axiom,
c_Nat_Osize__class_Osize(c_List_Oreplicate(X2,X1,X3),tc_List_Olist(X3)) = X2,
inference(unfold_definition,[status(thm)],[c_0_659,def_lhs_atom17]) ).
cnf(c_0_660_0,axiom,
c_Nat_Osize__class_Osize(c_List_Orotate(X2,X1,X3),tc_List_Olist(X3)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X3)),
inference(unfold_definition,[status(thm)],[c_0_660,def_lhs_atom12]) ).
cnf(c_0_661_0,axiom,
c_List_Orev(c_List_Oreplicate(X2,X1,X3),X3) = c_List_Oreplicate(X2,X1,X3),
inference(unfold_definition,[status(thm)],[c_0_661,def_lhs_atom9]) ).
cnf(c_0_662_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X2),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_662,def_lhs_atom140]) ).
cnf(c_0_663_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_663,def_lhs_atom119]) ).
cnf(c_0_664_0,axiom,
c_Type_Otyping(X2,c_Lambda_OdB_OVar(X1),hAPP(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_664,def_lhs_atom113]) ).
cnf(c_0_665_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(unfold_definition,[status(thm)],[c_0_665,def_lhs_atom111]) ).
cnf(c_0_666_0,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X2)),X1)),
inference(unfold_definition,[status(thm)],[c_0_666,def_lhs_atom109]) ).
cnf(c_0_667_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_667,def_lhs_atom108]) ).
cnf(c_0_668_0,axiom,
c_Lambda_OdB_OAbs(X2) != c_Lambda_OdB_OVar(X1),
inference(unfold_definition,[status(thm)],[c_0_668,def_lhs_atom107]) ).
cnf(c_0_669_0,axiom,
c_List_Olistrelp(X1,c_List_Olist_ONil(X2),c_List_Olist_ONil(X2),X2),
inference(unfold_definition,[status(thm)],[c_0_669,def_lhs_atom94]) ).
cnf(c_0_670_0,axiom,
c_List_Orotate(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
inference(unfold_definition,[status(thm)],[c_0_670,def_lhs_atom92]) ).
cnf(c_0_671_0,axiom,
c_List_Oremove1(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
inference(unfold_definition,[status(thm)],[c_0_671,def_lhs_atom88]) ).
cnf(c_0_672_0,axiom,
c_List_Ofilter(X1,c_List_Olist_ONil(X2),X2) = c_List_Olist_ONil(X2),
inference(unfold_definition,[status(thm)],[c_0_672,def_lhs_atom82]) ).
cnf(c_0_673_0,axiom,
c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),
inference(unfold_definition,[status(thm)],[c_0_673,def_lhs_atom73]) ).
cnf(c_0_674_0,axiom,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_674,def_lhs_atom72]) ).
cnf(c_0_675_0,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2)),X1)),c_Lambda_Osubst(X2,X1,c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(unfold_definition,[status(thm)],[c_0_675,def_lhs_atom69]) ).
cnf(c_0_676_0,axiom,
c_List_Orev(c_List_Orev(X1,X2),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_676,def_lhs_atom67]) ).
cnf(c_0_677_0,axiom,
c_List_Orev(c_List_Orev(X1,X2),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_677,def_lhs_atom68]) ).
cnf(c_0_678_0,axiom,
c_List_Orev(c_List_Orev(X1,X2),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_678,def_lhs_atom67]) ).
cnf(c_0_679_0,axiom,
c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),
inference(unfold_definition,[status(thm)],[c_0_679,def_lhs_atom58]) ).
cnf(c_0_680_0,axiom,
c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
inference(unfold_definition,[status(thm)],[c_0_680,def_lhs_atom54]) ).
cnf(c_0_681_0,axiom,
c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_681,def_lhs_atom52]) ).
cnf(c_0_682_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_682,def_lhs_atom53]) ).
cnf(c_0_683_0,axiom,
c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_683,def_lhs_atom52]) ).
cnf(c_0_684_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_684,def_lhs_atom51]) ).
cnf(c_0_685_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_685,def_lhs_atom51]) ).
cnf(c_0_686_0,axiom,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2) = c_Transitive__Closure_Ortranclp(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_686,def_lhs_atom41]) ).
cnf(c_0_687_0,axiom,
c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) = c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2),
inference(unfold_definition,[status(thm)],[c_0_687,def_lhs_atom40]) ).
cnf(c_0_688_0,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
inference(unfold_definition,[status(thm)],[c_0_688,def_lhs_atom21]) ).
cnf(c_0_689_0,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = c_List_Olist_ONil(X2),
inference(unfold_definition,[status(thm)],[c_0_689,def_lhs_atom21]) ).
cnf(c_0_690_0,axiom,
c_Nat_Osize__class_Osize(c_List_Orev(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),
inference(unfold_definition,[status(thm)],[c_0_690,def_lhs_atom20]) ).
cnf(c_0_691_0,axiom,
c_Lambda_OdB_OVar(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_691,def_lhs_atom122]) ).
cnf(c_0_692_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(X1),
inference(unfold_definition,[status(thm)],[c_0_692,def_lhs_atom118]) ).
cnf(c_0_693_0,axiom,
c_Lambda_OdB_OAbs(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_693,def_lhs_atom117]) ).
cnf(c_0_694_0,axiom,
X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(X1),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(X1),tc_Lambda_OdB,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_694,def_lhs_atom104]) ).
cnf(c_0_695_0,axiom,
c_List_Orev(c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
inference(unfold_definition,[status(thm)],[c_0_695,def_lhs_atom95]) ).
cnf(c_0_696_0,axiom,
c_List_Olist_ONil(X1) = c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1),
inference(unfold_definition,[status(thm)],[c_0_696,def_lhs_atom93]) ).
cnf(c_0_697_0,axiom,
c_List_Oremdups(c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
inference(unfold_definition,[status(thm)],[c_0_697,def_lhs_atom50]) ).
cnf(c_0_698_0,axiom,
c_List_Olist_ONil(X1) = c_List_Oremdups(c_List_Olist_ONil(X1),X1),
inference(unfold_definition,[status(thm)],[c_0_698,def_lhs_atom46]) ).
cnf(c_0_699_0,axiom,
c_List_Olist_ONil(X1) = c_List_Orev(c_List_Olist_ONil(X1),X1),
inference(unfold_definition,[status(thm)],[c_0_699,def_lhs_atom45]) ).
cnf(c_0_700_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X1),c_List_Olist_ONil(X1),X1) = c_List_Olist_ONil(X1),
inference(unfold_definition,[status(thm)],[c_0_700,def_lhs_atom44]) ).
cnf(c_0_701_0,axiom,
c_Nat_Osize__class_Osize(c_List_Olist_ONil(X1),tc_List_Olist(X1)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_701,def_lhs_atom22]) ).
cnf(c_0_702_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_702,def_lhs_atom14]) ).
cnf(c_0_703_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_703,def_lhs_atom13]) ).
cnf(c_0_704_0,axiom,
c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
inference(unfold_definition,[status(thm)],[c_0_704,def_lhs_atom11]) ).
cnf(c_0_705_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_705,def_lhs_atom6]) ).
cnf(c_0_706_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_706,def_lhs_atom5]) ).
cnf(c_0_707_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_List_Olist_ONil(X1),tc_List_Olist(X1)),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_707,def_lhs_atom2]) ).
cnf(c_0_708_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_708,def_lhs_atom139]) ).
cnf(c_0_709_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_709,def_lhs_atom138]) ).
cnf(c_0_710_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_710,def_lhs_atom137]) ).
cnf(c_0_711_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_711,def_lhs_atom136]) ).
cnf(c_0_712_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_712,def_lhs_atom135]) ).
cnf(c_0_713_0,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_713,def_lhs_atom134]) ).
cnf(c_0_714_0,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_714,def_lhs_atom133]) ).
cnf(c_0_715_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_715,def_lhs_atom132]) ).
cnf(c_0_716_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_716,def_lhs_atom131]) ).
cnf(c_0_717_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_717,def_lhs_atom130]) ).
cnf(c_0_718_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_718,def_lhs_atom129]) ).
cnf(c_0_719_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_719,def_lhs_atom128]) ).
cnf(c_0_720_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_720,def_lhs_atom127]) ).
cnf(c_0_721_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_721,def_lhs_atom126]) ).
cnf(c_0_722_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_722,def_lhs_atom125]) ).
cnf(c_0_723_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_723,def_lhs_atom124]) ).
cnf(c_0_724_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_724,def_lhs_atom16]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X34,X9,X20,X21,X22,X35,X23] :
( X22 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X23,X22,X21,X34),X23,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X22)
| ~ c_Type_Otypings(X21,X9,X35)
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X34,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
file('<stdin>',cls_var__app__types_0) ).
fof(c_0_1_002,axiom,
! [X27,X16,X17] :
( X27 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X17,X16,X27),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X16,tc_Lambda_OdB,tc_Lambda_OdB)),X27)) ),
file('<stdin>',cls_head__Var__reduction_1) ).
fof(c_0_2_003,axiom,
! [X34,X9,X20,X21,X22,X35,X23] :
( c_Type_Otypings(X21,X34,c_Type_Osko__Type__Xvar__app__types__1__1(X23,X22,X21,X34))
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X22)
| ~ c_Type_Otypings(X21,X9,X35)
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X34,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
file('<stdin>',cls_var__app__types_1) ).
fof(c_0_3_004,axiom,
! [X27,X16,X17] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X16,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X17,X16,X27),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X16,tc_Lambda_OdB,tc_Lambda_OdB)),X27)) ),
file('<stdin>',cls_head__Var__reduction_0) ).
fof(c_0_4_005,axiom,
! [X15,X31] :
( ~ hBOOL(hAPP(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X31)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X31),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X31)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X31),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(X31,X15)) ),
file('<stdin>',cls_lem_5) ).
fof(c_0_5_006,axiom,
! [X15,X31] :
( hBOOL(hAPP(X31,X15))
| ~ hBOOL(hAPP(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X31)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X31),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X31)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X31),tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('<stdin>',cls_Apps__dB__induct_5) ).
fof(c_0_6_007,axiom,
! [X6,X16,X10] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X16,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X6,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X16,X6,tc_Lambda_OdB) ),
file('<stdin>',cls_apps__preserves__betas_0) ).
fof(c_0_7_008,axiom,
! [X6,X7,X10] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X6,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X7)) ),
file('<stdin>',cls_apps__preserves__beta2_0) ).
fof(c_0_8_009,axiom,
! [X6,X7,X10] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X6,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X7)) ),
file('<stdin>',cls_apps__preserves__beta_0) ).
fof(c_0_9_010,axiom,
! [X6,X7,X10] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10)),X7),X6,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X10,X7,c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('<stdin>',cls_Beta_0) ).
fof(c_0_10_011,axiom,
! [X45,X29,X30,X33,X31] :
( ~ hBOOL(hAPP(X31,c_List_Olist_Olist__case(X30,X29,c_List_Olist_OCons(X33,X45,t_b),t_a,t_b)))
| hBOOL(hAPP(X31,hAPP(hAPP(X29,X33),X45))) ),
file('<stdin>',cls_list_Osplit_1) ).
fof(c_0_11_012,axiom,
! [X42,X25,X29,X30,X31] :
( ~ hBOOL(hAPP(X31,c_List_Olist_Olist__case(X30,X29,c_List_Olist_OCons(X25,X42,t_b),t_a,t_b)))
| hBOOL(hAPP(X31,hAPP(hAPP(X29,X25),X42))) ),
file('<stdin>',cls_list_Osplit__asm_1) ).
fof(c_0_12_013,axiom,
! [X41,X42,X28,X29,X30,X31] :
( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X30,X29,X28,hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41),t_a)))
| hBOOL(hAPP(X31,hAPP(hAPP(X29,X42),X41))) ),
file('<stdin>',cls_dB_Osplit__asm_1) ).
fof(c_0_13_014,axiom,
! [X28,X29,X30,X12,X14,X31] :
( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X30,X29,X28,hAPP(hAPP(c_Lambda_OdB_OApp,X14),X12),t_a)))
| hBOOL(hAPP(X31,hAPP(hAPP(X29,X14),X12))) ),
file('<stdin>',cls_dB_Osplit_1) ).
fof(c_0_14_015,axiom,
! [X15,X31] :
( hBOOL(hAPP(X31,c_ListApplication_Osko__ListApplication__Xlem__1__3(X31)))
| ~ hBOOL(hAPP(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X31)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X31),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(X31,X15)) ),
file('<stdin>',cls_lem_3) ).
fof(c_0_15_016,axiom,
! [X15,X31] :
( hBOOL(hAPP(X31,X15))
| hBOOL(hAPP(X31,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X31)))
| ~ hBOOL(hAPP(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X31)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X31),tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('<stdin>',cls_Apps__dB__induct_3) ).
fof(c_0_16_017,axiom,
! [X9,X20,X21,X22,X23] :
( X23 = X22
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X22)
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
file('<stdin>',cls_var__app__type__eq_0) ).
fof(c_0_17_018,axiom,
! [X28,X29,X30,X55,X31] :
( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X30,X29,X28,c_Lambda_OdB_OAbs(X55),t_a)))
| hBOOL(hAPP(X31,hAPP(X28,X55))) ),
file('<stdin>',cls_dB_Osplit_2) ).
fof(c_0_18_019,axiom,
! [X25,X28,X29,X30,X31] :
( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X30,X29,X28,c_Lambda_OdB_OAbs(X25),t_a)))
| hBOOL(hAPP(X31,hAPP(X28,X25))) ),
file('<stdin>',cls_dB_Osplit__asm_2) ).
fof(c_0_19_020,axiom,
! [X32,X28,X29,X30,X31] :
( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X30,X29,X28,c_Lambda_OdB_OVar(X32),t_a)))
| hBOOL(hAPP(X31,hAPP(X30,X32))) ),
file('<stdin>',cls_dB_Osplit__asm_0) ).
fof(c_0_20_021,axiom,
! [X19,X28,X29,X30,X31] :
( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X30,X29,X28,c_Lambda_OdB_OVar(X19),t_a)))
| hBOOL(hAPP(X31,hAPP(X30,X19))) ),
file('<stdin>',cls_dB_Osplit_0) ).
fof(c_0_21_022,axiom,
! [X29,X30,X31] :
( ~ hBOOL(hAPP(X31,c_List_Olist_Olist__case(X30,X29,c_List_Olist_ONil(t_b),t_a,t_b)))
| hBOOL(hAPP(X31,X30)) ),
file('<stdin>',cls_list_Osplit_0) ).
fof(c_0_22_023,axiom,
! [X6,X7,X10] :
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X10,X7,c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X7,tc_Lambda_OdB)
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10)),X7),X6,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
file('<stdin>',cls_double__induction__lemma_0) ).
fof(c_0_23_024,axiom,
! [X9,X20,X21,X23] :
( c_Type_Otyping(X21,c_Lambda_OdB_OVar(X20),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X23,X21,X20,X9),X23,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
file('<stdin>',cls_var__app__typesE_0) ).
fof(c_0_24_025,axiom,
! [X9,X15,X21,X23] :
( c_Type_Otyping(X21,X15,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X23,X21,X15,X9),X23,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X9,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
file('<stdin>',cls_list__app__typeD_0) ).
fof(c_0_25_026,axiom,
! [X9,X15,X21,X23] :
( c_Type_Otyping(X21,X15,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X23,X21,X15,X9),X23,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X9,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
file('<stdin>',cls_list__app__typeE_0) ).
fof(c_0_26_027,axiom,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X33),v_sko__InductTermi__XIT__Xcases__5(X33),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X33)))
| X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X33)),v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_IT_Ocases_4) ).
fof(c_0_27_028,axiom,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X33),v_sko__InductTermi__XIT__Xcases__5(X33),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)))
| X33 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X33))
| X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X33)),v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_IT_Ocases_1) ).
fof(c_0_28_029,axiom,
! [X26,X15,X7] :
( c_List_Oappend(X26,c_List_Olist_OCons(X7,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X26,tc_Lambda_OdB,tc_Lambda_OdB)),X7) = c_List_Ofoldl(c_Lambda_OdB_OApp,X15,c_List_Oappend(X26,c_List_Olist_OCons(X7,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
file('<stdin>',cls_App__eq__foldl__conv_3) ).
fof(c_0_29_030,axiom,
! [X9,X15,X21,X35,X23] :
( c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X9,tc_Lambda_OdB,tc_Lambda_OdB),X23)
| ~ c_Type_Otypings(X21,X9,X35)
| ~ c_Type_Otyping(X21,X15,c_List_Ofoldr(c_Type_Otype_OFun,X35,X23,tc_Type_Otype,tc_Type_Otype)) ),
file('<stdin>',cls_list__app__typeI_0) ).
fof(c_0_30_031,axiom,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X33),v_sko__InductTermi__XIT__Xcases__5(X33),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X33)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_IT_Ocases_10) ).
fof(c_0_31_032,axiom,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X33),v_sko__InductTermi__XIT__Xcases__5(X33),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)))
| X33 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X33))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_IT_Ocases_7) ).
fof(c_0_32_033,axiom,
! [X16,X17] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X16,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X16,tc_Lambda_OdB) ),
file('<stdin>',cls_IT_OVar_0) ).
fof(c_0_33_034,axiom,
! [X9,X20,X21,X23] :
( c_Type_Otypings(X21,X9,c_Type_Osko__Type__Xvar__app__typesE__1__1(X23,X21,X20,X9))
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
file('<stdin>',cls_var__app__typesE_1) ).
fof(c_0_34_035,axiom,
! [X9,X15,X21,X23] :
( c_Type_Otypings(X21,X9,c_Type_Osko__Type__Xlist__app__typeD__1__1(X23,X21,X15,X9))
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X9,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
file('<stdin>',cls_list__app__typeD_1) ).
fof(c_0_35_036,axiom,
! [X9,X15,X21,X23] :
( c_Type_Otypings(X21,X9,c_Type_Osko__Type__Xlist__app__typeE__1__1(X23,X21,X15,X9))
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X9,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
file('<stdin>',cls_list__app__typeE_1) ).
fof(c_0_36_037,axiom,
! [X6,X7,X16,X10] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),X16,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X10 = X7 ),
file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_0) ).
fof(c_0_37_038,axiom,
! [X6,X7,X16,X10] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),X16,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X16 = X6 ),
file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_1) ).
fof(c_0_38_039,axiom,
! [X6,X16,X17,X8] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X16,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X8 = X17 ),
file('<stdin>',cls_Var__apps__eq__Var__apps__conv_0) ).
fof(c_0_39_040,axiom,
! [X6,X16,X17,X8] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X16,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X16 = X6 ),
file('<stdin>',cls_Var__apps__eq__Var__apps__conv_1) ).
fof(c_0_40_041,axiom,
! [X36,X39,X26,X3] :
( ~ class_OrderedGroup_Osemigroup__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X39),X36,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X39,X36,X3,X3)) ),
file('<stdin>',cls_foldl__assoc_0) ).
fof(c_0_41_042,axiom,
! [X9,X7,X10] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X9,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB)
| X10 = X7 ),
file('<stdin>',cls_apps__eq__tail__conv_0) ).
fof(c_0_42_043,axiom,
! [X36,X39,X26,X38,X3] :
( c_List_Ofoldl(X38,hAPP(hAPP(X38,X26),X39),X36,X3,X3) = hAPP(hAPP(X38,X26),c_List_Ofoldl(X38,X39,X36,X3,X3))
| ~ c_OrderedGroup_Osemigroup__add(X38,X3) ),
file('<stdin>',cls_semigroup__add_Ofoldl__assoc_0) ).
fof(c_0_43_044,axiom,
! [X36,X37,X26,X38,X3] :
( hAPP(hAPP(X38,X26),c_List_Ofoldl(X38,X37,X36,X3,X3)) = c_List_Ofoldl(X38,X26,X36,X3,X3)
| ~ c_OrderedGroup_Omonoid__add(X37,X38,X3) ),
file('<stdin>',cls_monoid__add_Ofoldl__absorb0_0) ).
fof(c_0_44_045,axiom,
! [X43,X33,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X33,X43,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X43,c_HOL_Ozero__class_Ozero(X3),X3,X3)) ),
file('<stdin>',cls_foldl__foldr1__lemma_0) ).
fof(c_0_45_046,axiom,
! [X36,X26,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X36,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X26,X36,X3,X3) ),
file('<stdin>',cls_foldl__absorb0_0) ).
fof(c_0_46_047,axiom,
! [X9,X15,X7,X10] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X10),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X9,tc_Lambda_OdB,tc_Lambda_OdB)
| X10 = c_List_Ofoldl(c_Lambda_OdB_OApp,X15,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X10,X7,X15,X9),tc_Lambda_OdB,tc_Lambda_OdB)
| X9 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_App__eq__foldl__conv_2) ).
fof(c_0_47_048,axiom,
! [X25,X7,X10] :
( X10 != c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X10),X7),X25,tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X10),X7) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X10),X7),c_List_Oappend(X25,c_List_Olist_OCons(X7,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
file('<stdin>',cls_App__eq__foldl__conv_5) ).
fof(c_0_48_049,axiom,
! [X33] :
( X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X33))),v_sko__InductTermi__XIT__Xcases__5(X33)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X33)))
| X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X33)),v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_IT_Ocases_3) ).
fof(c_0_49_050,axiom,
! [X33] :
( X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X33))),v_sko__InductTermi__XIT__Xcases__5(X33)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| X33 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X33))
| X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X33)),v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_IT_Ocases_0) ).
fof(c_0_50_051,axiom,
! [X9,X15,X7,X10] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X10),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X9,tc_Lambda_OdB,tc_Lambda_OdB)
| X9 = c_List_Oappend(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X10,X7,X15,X9),c_List_Olist_OCons(X7,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)
| X9 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_App__eq__foldl__conv_1) ).
fof(c_0_51_052,axiom,
! [X36,X48,X43,X8,X63,X3] :
( c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3)) != c_Nat_Osize__class_Osize(X48,tc_List_Olist(X63))
| c_Map_Omap__upds(X8,c_List_Oappend(X43,X36,X3),X48,X3,X63) = c_Map_Omap__upds(X8,X43,X48,X3,X63) ),
file('<stdin>',cls_fun__upds__append__drop_0) ).
fof(c_0_52_053,axiom,
! [X36,X48,X43,X8,X63,X3] :
( c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3)) != c_Nat_Osize__class_Osize(X48,tc_List_Olist(X63))
| c_Map_Omap__upds(X8,X43,c_List_Oappend(X48,X36,X63),X3,X63) = c_Map_Omap__upds(X8,X43,X48,X3,X63) ),
file('<stdin>',cls_fun__upds__append2__drop_0) ).
fof(c_0_53_054,axiom,
! [X43,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X43,X3,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X43,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
file('<stdin>',cls_foldl__foldr1_0) ).
fof(c_0_54_055,axiom,
! [X43,X33,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X43,X33,X3,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X33,X43,X3,X3) ),
file('<stdin>',cls_foldr__conv__foldl_0) ).
fof(c_0_55_056,axiom,
! [X15,X7,X10] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X10),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X15,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X10),X7) = X15 ),
file('<stdin>',cls_App__eq__foldl__conv_0) ).
fof(c_0_56_057,axiom,
! [X6,X7,X10] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X10)
| X7 = c_Lambda_OdB_OAbs(X10) ),
file('<stdin>',cls_apps__eq__Abs__conv_0) ).
fof(c_0_57_058,axiom,
! [X6,X7,X10] :
( c_Lambda_OdB_OAbs(X10) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X10) = X7 ),
file('<stdin>',cls_Abs__eq__apps__conv_0) ).
fof(c_0_58_059,axiom,
! [X6,X7,X8] :
( c_Lambda_OdB_OVar(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X8) = X7 ),
file('<stdin>',cls_Var__eq__apps__conv_0) ).
fof(c_0_59_060,axiom,
! [X6,X7,X10] :
( c_Lambda_OdB_OAbs(X10) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X6 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_Abs__eq__apps__conv_1) ).
fof(c_0_60_061,axiom,
! [X6,X7,X10] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X10)
| X6 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_apps__eq__Abs__conv_1) ).
fof(c_0_61_062,axiom,
! [X6,X7,X8] :
( c_Lambda_OdB_OVar(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X6 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_Var__eq__apps__conv_1) ).
fof(c_0_62_063,axiom,
! [X39,X26,X10,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X39),X26))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X10,X3,X3),X3),X26),X39)) ),
file('<stdin>',cls_rtranclp__converseD_0) ).
fof(c_0_63_064,axiom,
! [X48,X39,X43,X26,X10,X3] :
( hBOOL(hAPP(hAPP(X10,X39),X26))
| c_ListOrder_Ostep1(X10,X48,X43,X3)
| ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X48,c_List_Olist_OCons(X39,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3),X3),X3) ),
file('<stdin>',cls_Snoc__step1__SnocD_1) ).
fof(c_0_64_065,axiom,
! [X48,X39,X43,X26,X10,X3] :
( X48 = X43
| c_ListOrder_Ostep1(X10,X48,X43,X3)
| ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X48,c_List_Olist_OCons(X39,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3),X3),X3) ),
file('<stdin>',cls_Snoc__step1__SnocD_0) ).
fof(c_0_65_066,axiom,
! [X48,X39,X43,X26,X10,X3] :
( hBOOL(hAPP(hAPP(X10,X39),X26))
| X39 = X26
| ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X48,c_List_Olist_OCons(X39,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3),X3),X3) ),
file('<stdin>',cls_Snoc__step1__SnocD_3) ).
fof(c_0_66_067,axiom,
! [X33] :
( X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X33))),v_sko__InductTermi__XIT__Xcases__5(X33)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X33)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_IT_Ocases_9) ).
fof(c_0_67_068,axiom,
! [X43,X50,X26,X51,X20,X3] :
( c_List_Olist__update(c_List_Olist__update(X43,X20,X26,X3),X51,X50,X3) = c_List_Olist__update(c_List_Olist__update(X43,X51,X50,X3),X20,X26,X3)
| X20 = X51 ),
file('<stdin>',cls_list__update__swap_0) ).
fof(c_0_68_069,axiom,
! [X48,X39,X43,X26,X10,X3] :
( X48 = X43
| X39 = X26
| ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X48,c_List_Olist_OCons(X39,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3),X3),X3) ),
file('<stdin>',cls_Snoc__step1__SnocD_2) ).
fof(c_0_69_070,axiom,
! [X33] :
( X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X33))),v_sko__InductTermi__XIT__Xcases__5(X33)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| X33 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X33))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_IT_Ocases_6) ).
fof(c_0_70_071,axiom,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X33)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X33)))
| X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X33)),v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_IT_Ocases_5) ).
fof(c_0_71_072,axiom,
! [X39,X26,X10,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X10,X3,X3),X3),X26),X39))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X39),X26)) ),
file('<stdin>',cls_rtranclp__converseI_0) ).
fof(c_0_72_073,axiom,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X33)))
| X33 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X33))
| X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X33)),v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_IT_Ocases_2) ).
fof(c_0_73_074,axiom,
! [X9,X15,X21,X35] :
( c_Type_Otypings(X21,X9,c_Type_Osko__Type__Xtypes__snocE__1__1(X35,X21,X15,X9))
| ~ c_Type_Otypings(X21,c_List_Oappend(X9,c_List_Olist_OCons(X15,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X35) ),
file('<stdin>',cls_types__snocE_1) ).
fof(c_0_74_075,axiom,
! [X9,X15,X21,X35] :
( c_Type_Otyping(X21,X15,c_Type_Osko__Type__Xtypes__snocE__1__2(X35,X21,X15,X9))
| ~ c_Type_Otypings(X21,c_List_Oappend(X9,c_List_Olist_OCons(X15,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X35) ),
file('<stdin>',cls_types__snocE_2) ).
fof(c_0_75_076,axiom,
! [X52,X15,X59,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X15)),hAPP(hAPP(c_Lambda_OdB_OApp,X59),X52)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X15),X52))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X59)) ),
file('<stdin>',cls_rtrancl__beta__App_0) ).
fof(c_0_76_077,axiom,
! [X15,X7,X10,X20] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X10,X15,X20)),c_Lambda_Osubst(X7,X15,X20)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X7)) ),
file('<stdin>',cls_subst__preserves__beta_H_0) ).
fof(c_0_77_078,axiom,
! [X15,X7,X10,X20] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X15,X10,X20)),c_Lambda_Osubst(X15,X7,X20)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X7)) ),
file('<stdin>',cls_subst__preserves__beta2_H_0) ).
fof(c_0_78_079,axiom,
! [X48,X39,X43,X26,X10,X3] :
( c_ListOrder_Ostep1(X10,X48,X43,X3)
| hBOOL(hAPP(hAPP(X10,X39),X26))
| ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X39,X48,X3),c_List_Olist_OCons(X26,X43,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_1) ).
fof(c_0_79_080,axiom,
! [X48,X43,X26,X17,X3] :
( c_List_Olist__update(c_List_Oappend(X43,X48,X3),X17,X26,X3) = c_List_Oappend(c_List_Olist__update(X43,X17,X26,X3),X48,X3)
| ~ c_HOL_Oord__class_Oless(X17,c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3)),tc_nat) ),
file('<stdin>',cls_list__update__append_0) ).
fof(c_0_80_081,axiom,
! [X48,X43,X26,X20,X3] :
( c_List_Olist__update(c_List_Oappend(X43,X48,X3),X20,X26,X3) = c_List_Oappend(c_List_Olist__update(X43,X20,X26,X3),X48,X3)
| ~ c_HOL_Oord__class_Oless(X20,c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3)),tc_nat) ),
file('<stdin>',cls_list__update__append1_0) ).
fof(c_0_81_082,axiom,
! [X48,X39,X43,X26,X10,X3] :
( c_List_Olistrelp(X10,c_List_Olist_OCons(X26,X43,X3),c_List_Olist_OCons(X39,X48,X3),X3)
| ~ c_List_Olistrelp(X10,X43,X48,X3)
| ~ hBOOL(hAPP(hAPP(X10,X26),X39)) ),
file('<stdin>',cls_listrelp_OCons_0) ).
fof(c_0_82_083,axiom,
! [X48,X39,X43,X26,X10,X3] :
( c_ListOrder_Ostep1(X10,X48,X43,X3)
| X43 = X48
| ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X39,X48,X3),c_List_Olist_OCons(X26,X43,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_3) ).
fof(c_0_83_084,axiom,
! [X15,X7,X10,X20] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X15,X10,X20)),c_Lambda_Osubst(X15,X7,X20)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X7)) ),
file('<stdin>',cls_subst__preserves__beta2_0) ).
fof(c_0_84_085,axiom,
! [X10,X47,X33,X63,X3] :
( hBOOL(hAPP(hAPP(X10,X47),X33))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X3,X63),X33),X47)) ),
file('<stdin>',cls_conversepD_0) ).
fof(c_0_85_086,axiom,
! [X10,X69,X70,X63,X3] :
( hBOOL(hAPP(hAPP(X10,X69),X70))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X3,X63),X70),X69)) ),
file('<stdin>',cls_conversep_Ocases_0) ).
fof(c_0_86_087,axiom,
! [X48,X43,X26,X10,X3] :
( ~ c_ListOrder_Ostep1(X10,X48,X43,X3)
| c_ListOrder_Ostep1(X10,c_List_Oappend(X48,X26,X3),c_List_Oappend(X43,X26,X3),X3) ),
file('<stdin>',cls_append__step1I_0) ).
fof(c_0_87_088,axiom,
! [X26,X60,X34,X10,X3] :
( c_ListOrder_Ostep1(X10,c_List_Oappend(X26,X60,X3),c_List_Oappend(X26,X34,X3),X3)
| ~ c_ListOrder_Ostep1(X10,X60,X34,X3) ),
file('<stdin>',cls_append__step1I_1) ).
fof(c_0_88_089,axiom,
! [X48,X43,X26,X10,X3] :
( c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X26,X48,X3),c_List_Olist_OCons(X26,X43,X3),X3)
| ~ c_ListOrder_Ostep1(X10,X48,X43,X3) ),
file('<stdin>',cls_Cons__step1__Cons_5) ).
fof(c_0_89_090,axiom,
! [X15,X59,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X15)),hAPP(hAPP(c_Lambda_OdB_OApp,X59),X15)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X59)) ),
file('<stdin>',cls_rtrancl__beta__AppL_0) ).
fof(c_0_90_091,axiom,
! [X52,X15,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X15)),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X52)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X15),X52)) ),
file('<stdin>',cls_rtrancl__beta__AppR_0) ).
fof(c_0_91_092,axiom,
! [X15,X7,X10,X20] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X10,X15,X20)),c_Lambda_Osubst(X7,X15,X20)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X7)) ),
file('<stdin>',cls_subst__preserves__beta_0) ).
fof(c_0_92_093,axiom,
! [X42,X25,X26,X31,X3] :
( ~ hBOOL(hAPP(X31,X26))
| hBOOL(hAPP(X31,c_List_Osko__List__XCons__eq__filter__iff__1__3(X31,X25,X3)))
| c_List_Olist_OCons(X26,c_List_Ofilter(X31,X42,X3),X3) = c_List_Ofilter(X31,c_List_Oappend(X25,c_List_Olist_OCons(X26,X42,X3),X3),X3) ),
file('<stdin>',cls_Cons__eq__filter__iff_5) ).
fof(c_0_93_094,axiom,
! [X42,X25,X26,X31,X3] :
( ~ hBOOL(hAPP(X31,X26))
| hBOOL(hAPP(X31,c_List_Osko__List__Xfilter__eq__Cons__iff__1__3(X31,X25,X3)))
| c_List_Ofilter(X31,c_List_Oappend(X25,c_List_Olist_OCons(X26,X42,X3),X3),X3) = c_List_Olist_OCons(X26,c_List_Ofilter(X31,X42,X3),X3) ),
file('<stdin>',cls_filter__eq__Cons__iff_5) ).
fof(c_0_94_095,axiom,
! [X48,X43,X62,X63,X3] :
( c_List_Omap(X62,X43,X63,X3) != c_List_Omap(X62,X48,X63,X3)
| c_Nat_Osize__class_Osize(X43,tc_List_Olist(X63)) = c_Nat_Osize__class_Osize(X48,tc_List_Olist(X63)) ),
file('<stdin>',cls_map__eq__imp__length__eq_0) ).
fof(c_0_95_096,axiom,
! [X48,X39,X43,X26,X10,X3] :
( X26 = X39
| hBOOL(hAPP(hAPP(X10,X39),X26))
| ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X39,X48,X3),c_List_Olist_OCons(X26,X43,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_0) ).
fof(c_0_96_097,axiom,
! [X58,X39,X26,X10,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X26),X58))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X39),X58))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X26),X39)) ),
file('<stdin>',cls_rtranclp__trans_0) ).
fof(c_0_97_098,axiom,
! [X48,X39,X43,X26,X10,X3] :
( X26 = X39
| X43 = X48
| ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X39,X48,X3),c_List_Olist_OCons(X26,X43,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_2) ).
fof(c_0_98_099,axiom,
! [X61,X46,X47,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X61)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X61)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_99_100,axiom,
! [X36,X39,X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X39,X36,X3),X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X26,c_List_Olist_OCons(X39,X36,X3),X3),X3) ),
file('<stdin>',cls_sorted_Osimps_I3_J_1) ).
fof(c_0_100_101,axiom,
! [X10,X47,X33,X63,X3] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X3,X63),X33),X47))
| ~ hBOOL(hAPP(hAPP(X10,X47),X33)) ),
file('<stdin>',cls_conversep__iff_1) ).
fof(c_0_101_102,axiom,
! [X10,X47,X33,X63,X3] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X3,X63),X47),X33))
| ~ hBOOL(hAPP(hAPP(X10,X33),X47)) ),
file('<stdin>',cls_conversep_Ointros_0) ).
fof(c_0_102_103,axiom,
! [X40,X15,X7] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X40),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X40),X15)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X15)) ),
file('<stdin>',cls_appR_0) ).
fof(c_0_103_104,axiom,
! [X40,X15,X7] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X40)),hAPP(hAPP(c_Lambda_OdB_OApp,X15),X40)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X15)) ),
file('<stdin>',cls_appL_0) ).
fof(c_0_104_105,axiom,
! [X10,X46,X47,X33,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X33),X46))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X47),X46))
| ~ hBOOL(hAPP(hAPP(X10,X33),X47)) ),
file('<stdin>',cls_converse__rtranclp__into__rtranclp_0) ).
fof(c_0_105_106,axiom,
! [X10,X46,X47,X33,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X33),X46))
| ~ hBOOL(hAPP(hAPP(X10,X47),X46))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X33),X47)) ),
file('<stdin>',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
fof(c_0_106_107,axiom,
! [X39,X25,X26,X10,X3] :
( ~ hBOOL(hAPP(hAPP(X10,X39),X25))
| c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X39,X26,X3),c_List_Olist_OCons(X25,X26,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_4) ).
fof(c_0_107_108,axiom,
! [X7,X10,X20] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X10,X20)),c_Lambda_Olift(X7,X20)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X7)) ),
file('<stdin>',cls_lift__preserves__beta_H_0) ).
fof(c_0_108_109,axiom,
! [X48,X39,X43,X26,X3] :
( c_List_Oappend(X43,c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X48,c_List_Olist_OCons(X39,c_List_Olist_ONil(X3),X3),X3)
| X43 = X48 ),
file('<stdin>',cls_append1__eq__conv_0) ).
fof(c_0_109_110,axiom,
! [X48,X39,X43,X26,X3] :
( c_List_Oappend(X43,c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X48,c_List_Olist_OCons(X39,c_List_Olist_ONil(X3),X3),X3)
| X26 = X39 ),
file('<stdin>',cls_append1__eq__conv_1) ).
fof(c_0_110_111,axiom,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| ~ hBOOL(hAPP(X31,c_List_Olist_OCons(v_sko__List__Xconcat__Xinduct__1(X31),v_sko__List__Xconcat__Xinduct__2(X31),t_a)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
file('<stdin>',cls_concat_Oinduct_1) ).
fof(c_0_111_112,axiom,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| ~ hBOOL(hAPP(X31,c_List_Olist_OCons(v_sko__List__Xtake__Xinduct__1(X31),v_sko__List__Xtake__Xinduct__2(X31),t_a)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
file('<stdin>',cls_take_Oinduct_1) ).
fof(c_0_112_113,axiom,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| ~ hBOOL(hAPP(X31,c_List_Olist_OCons(v_sko__List__Xmap__Xinduct__1(X31),v_sko__List__Xmap__Xinduct__2(X31),t_a)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
file('<stdin>',cls_map_Oinduct_1) ).
fof(c_0_113_114,axiom,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| ~ hBOOL(hAPP(X31,c_List_Olist_OCons(v_sko__List__Xlist__Xinduct__1(X31),v_sko__List__Xlist__Xinduct__2(X31),t_a)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
file('<stdin>',cls_list_Oinduct_1) ).
fof(c_0_114_115,axiom,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| ~ hBOOL(hAPP(X31,c_List_Olist_OCons(v_sko__List__XdropWhile__Xinduct__1(X31),v_sko__List__XdropWhile__Xinduct__2(X31),t_a)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
file('<stdin>',cls_dropWhile_Oinduct_1) ).
fof(c_0_115_116,axiom,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| ~ hBOOL(hAPP(X31,c_List_Olist_OCons(v_sko__List__Xremove1__Xinduct__1(X31),v_sko__List__Xremove1__Xinduct__2(X31),t_a)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
file('<stdin>',cls_remove1_Oinduct_1) ).
fof(c_0_116_117,axiom,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| ~ hBOOL(hAPP(X31,c_List_Olist_OCons(v_sko__List__Xdistinct__Xinduct__1(X31),v_sko__List__Xdistinct__Xinduct__2(X31),t_a)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
file('<stdin>',cls_distinct_Oinduct_1) ).
fof(c_0_117_118,axiom,
! [X46,X47,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47)),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46)),X47) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_118_119,axiom,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X33,X47,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X46),X3) ),
file('<stdin>',cls_add__less__cancel__right_0) ).
fof(c_0_119_120,axiom,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X33,X47,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X47),X3) ),
file('<stdin>',cls_add__less__cancel__left_0) ).
fof(c_0_120_121,axiom,
! [X59,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X7)),c_Lambda_OdB_OAbs(X59)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X59)) ),
file('<stdin>',cls_rtrancl__beta__Abs_0) ).
fof(c_0_121_122,axiom,
! [X61,X46,X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X61),X3)
| ~ c_HOL_Oord__class_Oless(X46,X61,X3)
| ~ c_HOL_Oord__class_Oless(X33,X47,X3) ),
file('<stdin>',cls_add__strict__mono_0) ).
fof(c_0_122_123,axiom,
! [X10,X47,X33,X3] :
( c_Wellfounded_Oaccp(X10,X47,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X47),X33))
| ~ c_Wellfounded_Oaccp(X10,X33,X3) ),
file('<stdin>',cls_accp__downwards_0) ).
fof(c_0_123_124,axiom,
! [X10,X47,X33,X3] :
( c_Wellfounded_Oaccp(X10,X47,X3)
| ~ c_Wellfounded_Oaccp(X10,X33,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X47),X33)) ),
file('<stdin>',cls_accp__downwards__aux_0) ).
fof(c_0_124_125,axiom,
! [X46,X47,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47)),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X46)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_125_126,axiom,
! [X61,X46,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X61)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46)),X61) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_126_127,axiom,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47)),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X46)) ),
file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(c_0_127_128,axiom,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47)),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X46)) ),
file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).
fof(c_0_128_129,axiom,
! [X58,X39,X26,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X39),X58)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X39)),X58) ),
file('<stdin>',cls_class__semiring_Oadd__a_0) ).
fof(c_0_129_130,axiom,
! [X15,X7,X64,X22,X23] :
( c_Type_Otyping(X64,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X15),X22)
| ~ c_Type_Otyping(X64,X15,X23)
| ~ c_Type_Otyping(X64,X7,hAPP(hAPP(c_Type_Otype_OFun,X23),X22)) ),
file('<stdin>',cls_App_0) ).
fof(c_0_130_131,axiom,
! [X43,X62,X63,X3] :
( c_List_Omap(X62,X43,X63,X3) != c_List_Olist_ONil(X3)
| X43 = c_List_Olist_ONil(X63) ),
file('<stdin>',cls_map__is__Nil__conv_0) ).
fof(c_0_131_132,axiom,
! [X43,X62,X63,X3] :
( c_List_Olist_ONil(X3) != c_List_Omap(X62,X43,X63,X3)
| X43 = c_List_Olist_ONil(X63) ),
file('<stdin>',cls_Nil__is__map__conv_0) ).
fof(c_0_132_133,axiom,
! [X43,X26,X44,X3] :
( c_List_Olist__update(X43,X44,X26,X3) != c_List_Olist_ONil(X3)
| X43 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_list__update__nonempty_0) ).
fof(c_0_133_134,axiom,
! [X52,X15,X21,X23] :
( c_Type_Otyping(X21,X52,X23)
| ~ c_Type_Otyping(X21,X15,X23)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X15),X52)) ),
file('<stdin>',cls_subject__reduction_H_0) ).
fof(c_0_134_135,axiom,
! [X58,X39,X26,X40,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X39),X58)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X39),X40)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X58) = X40 ),
file('<stdin>',cls_add__cancel__21_0) ).
fof(c_0_135_136,axiom,
! [X43,X26,X31,X3] :
( c_List_Ofilter(X31,c_List_Olist_OCons(X26,X43,X3),X3) = c_List_Olist_OCons(X26,c_List_Ofilter(X31,X43,X3),X3)
| ~ hBOOL(hAPP(X31,X26)) ),
file('<stdin>',cls_filter_Osimps_I2_J_0) ).
fof(c_0_136_137,axiom,
! [X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X47,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_add__neg__neg_0) ).
fof(c_0_137_138,axiom,
! [X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X47,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
file('<stdin>',cls_add__pos__pos_0) ).
fof(c_0_138_139,axiom,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X46),X3)
| ~ c_HOL_Oord__class_Oless(X33,X47,X3) ),
file('<stdin>',cls_add__strict__right__mono_0) ).
fof(c_0_139_140,axiom,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X46),X3)
| ~ c_HOL_Oord__class_Oless(X33,X47,X3) ),
file('<stdin>',cls_add__less__cancel__right_1) ).
fof(c_0_140_141,axiom,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X47),X3)
| ~ c_HOL_Oord__class_Oless(X33,X47,X3) ),
file('<stdin>',cls_add__strict__left__mono_0) ).
fof(c_0_141_142,axiom,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X47),X3)
| ~ c_HOL_Oord__class_Oless(X33,X47,X3) ),
file('<stdin>',cls_add__less__cancel__left_1) ).
fof(c_0_142_143,axiom,
! [X7,X10,X20] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X10,X20)),c_Lambda_Olift(X7,X20)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X7)) ),
file('<stdin>',cls_lift__preserves__beta_0) ).
fof(c_0_143_144,axiom,
! [X46,X47,X33,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X47,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46),X3)
| ~ c_HOL_Oord__class_Oless(X47,X46,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
file('<stdin>',cls_pos__add__strict_0) ).
fof(c_0_144_145,axiom,
! [X38,X46,X47,X33,X3] :
( hAPP(hAPP(X38,hAPP(hAPP(X38,X33),X47)),X46) = hAPP(hAPP(X38,X33),hAPP(hAPP(X38,X47),X46))
| ~ c_OrderedGroup_Osemigroup__add(X38,X3) ),
file('<stdin>',cls_semigroup__add_Oadd__assoc_0) ).
fof(c_0_145_146,axiom,
! [X48,X43,X56,X3] :
( c_List_Olistsp(X56,c_List_Oappend(X43,X48,X3),X3)
| ~ c_List_Olistsp(X56,X48,X3)
| ~ c_List_Olistsp(X56,X43,X3) ),
file('<stdin>',cls_append__in__listsp__conv_2) ).
fof(c_0_146_147,axiom,
! [X39,X43,X26,X3] :
( c_List_Oremove1(X26,c_List_Olist_OCons(X39,X43,X3),X3) = c_List_Olist_OCons(X39,c_List_Oremove1(X26,X43,X3),X3)
| X26 = X39 ),
file('<stdin>',cls_remove1_Osimps_I2_J_1) ).
fof(c_0_147_148,axiom,
! [X33,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),X3) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(c_0_148_149,axiom,
! [X33,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(c_0_149_150,axiom,
! [X33,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_even__less__0__iff_0) ).
fof(c_0_150_151,axiom,
! [X61,X46,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X61)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X61)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_151_152,axiom,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X46)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46)) ),
file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(c_0_152_153,axiom,
! [X58,X39,X26,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X39),X58)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X39),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X58)) ),
file('<stdin>',cls_add__cancel__21_1) ).
fof(c_0_153_154,axiom,
! [X39,X26,X10,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X26),X39))
| ~ hBOOL(hAPP(hAPP(X10,X26),X39)) ),
file('<stdin>',cls_r__into__rtranclp_0) ).
fof(c_0_154_155,axiom,
! [X48,X43,X56,X3] :
( c_List_Olistsp(X56,X43,X3)
| ~ c_List_Olistsp(X56,c_List_Oappend(X43,X48,X3),X3) ),
file('<stdin>',cls_append__in__listsp__conv_0) ).
fof(c_0_155_156,axiom,
! [X48,X43,X56,X3] :
( c_List_Olistsp(X56,X48,X3)
| ~ c_List_Olistsp(X56,c_List_Oappend(X43,X48,X3),X3) ),
file('<stdin>',cls_append__in__listsp__conv_1) ).
fof(c_0_156_157,axiom,
! [X10,X24,X20] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X10,c_Lambda_OdB_OVar(X20),X24)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X10)) ),
file('<stdin>',cls_subst__Var__IT_0) ).
fof(c_0_157_158,axiom,
! [X48,X39,X43,X3] :
( c_List_Orev(X43,X3) != c_List_Olist_OCons(X39,X48,X3)
| X43 = c_List_Oappend(c_List_Orev(X48,X3),c_List_Olist_OCons(X39,c_List_Olist_ONil(X3),X3),X3) ),
file('<stdin>',cls_rev__eq__Cons__iff_0) ).
fof(c_0_158_159,axiom,
! [X39,X10,X33,X3] :
( c_Wellfounded_Oaccp(X10,X39,X3)
| ~ hBOOL(hAPP(hAPP(X10,X39),X33))
| ~ c_Wellfounded_Oaccp(X10,X33,X3) ),
file('<stdin>',cls_accp_Ocases_0) ).
fof(c_0_159_160,axiom,
! [X10,X47,X33,X3] :
( c_Wellfounded_Oaccp(X10,X33,X3)
| ~ hBOOL(hAPP(hAPP(X10,X33),X47))
| ~ c_Wellfounded_Oaccp(X10,X47,X3) ),
file('<stdin>',cls_accp__downward_0) ).
fof(c_0_160_161,axiom,
! [X33,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(c_0_161_162,axiom,
! [X33,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(c_0_162_163,axiom,
! [X33,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_even__less__0__iff_1) ).
fof(c_0_163_164,axiom,
! [X10] :
( hBOOL(hAPP(c_InductTermi_OIT,X10))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X10,tc_Lambda_OdB) ),
file('<stdin>',cls_termi__implies__IT_0) ).
fof(c_0_164_165,axiom,
! [X26,X17,X31,X3] :
( c_List_Ofilter(X31,c_List_Oreplicate(X17,X26,X3),X3) = c_List_Oreplicate(X17,X26,X3)
| ~ hBOOL(hAPP(X31,X26)) ),
file('<stdin>',cls_filter__replicate_0) ).
fof(c_0_165_166,axiom,
! [X52,X15,X21,X23] :
( c_Type_Otyping(X21,X52,X23)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X15),X52))
| ~ c_Type_Otyping(X21,X15,X23) ),
file('<stdin>',cls_subject__reduction_0) ).
fof(c_0_166_167,axiom,
! [X43,X26,X31,X3] :
( c_List_Oremove1(X26,c_List_Ofilter(X31,X43,X3),X3) = c_List_Ofilter(X31,X43,X3)
| hBOOL(hAPP(X31,X26)) ),
file('<stdin>',cls_remove1__filter__not_0) ).
fof(c_0_167_168,axiom,
! [X43,X26,X31,X3] :
( c_List_Ofilter(X31,c_List_Olist_OCons(X26,X43,X3),X3) = c_List_Ofilter(X31,X43,X3)
| hBOOL(hAPP(X31,X26)) ),
file('<stdin>',cls_filter_Osimps_I2_J_1) ).
fof(c_0_168_169,axiom,
! [X58,X39,X26,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X58,X26,X3)
| ~ c_HOL_Oord__class_Oless(X58,X39,X3)
| ~ c_HOL_Oord__class_Oless(X39,X26,X3) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_169_170,axiom,
! [X58,X39,X26,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X26,X58,X3)
| ~ c_HOL_Oord__class_Oless(X39,X58,X3)
| ~ c_HOL_Oord__class_Oless(X26,X39,X3) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_170_171,axiom,
! [X15,X7] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X7)),c_Lambda_OdB_OAbs(X15)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X15)) ),
file('<stdin>',cls_abs_0) ).
fof(c_0_171_172,axiom,
! [X43,X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(X43,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X26,X43,X3),X3) ),
file('<stdin>',cls_sorted__Cons_0) ).
fof(c_0_172_173,axiom,
! [X48,X43,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(X43,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X43,X48,X3),X3) ),
file('<stdin>',cls_sorted__append_0) ).
fof(c_0_173_174,axiom,
! [X48,X43,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(X48,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X43,X48,X3),X3) ),
file('<stdin>',cls_sorted__append_1) ).
fof(c_0_174_175,axiom,
! [X48,X43,X26,X31,X3] :
( c_List_Olist_OCons(X26,X43,X3) != c_List_Ofilter(X31,X48,X3)
| hBOOL(hAPP(X31,X26)) ),
file('<stdin>',cls_Cons__eq__filterD_2) ).
fof(c_0_175_176,axiom,
! [X48,X43,X26,X31,X3] :
( c_List_Ofilter(X31,X48,X3) != c_List_Olist_OCons(X26,X43,X3)
| hBOOL(hAPP(X31,X26)) ),
file('<stdin>',cls_filter__eq__ConsD_2) ).
fof(c_0_176_177,axiom,
! [X26,X17,X31,X3] :
( c_List_Ofilter(X31,c_List_Oreplicate(X17,X26,X3),X3) = c_List_Olist_ONil(X3)
| hBOOL(hAPP(X31,X26)) ),
file('<stdin>',cls_filter__replicate_1) ).
fof(c_0_177_178,axiom,
! [X15] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X15,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X15)) ),
file('<stdin>',cls_IT__implies__termi_0) ).
fof(c_0_178_179,axiom,
! [X17,X8,X31] :
( hBOOL(hAPP(hAPP(X31,X17),X8))
| c_HOL_Oord__class_Oless(X17,X8,tc_nat)
| X8 = X17
| c_HOL_Oord__class_Oless(X8,X17,tc_nat) ),
file('<stdin>',cls_nat__less__cases_0) ).
fof(c_0_179_180,axiom,
! [X58,X39,X26,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X39) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X58)
| X39 = X58 ),
file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).
fof(c_0_180_181,axiom,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X33)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X33)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_IT_Ocases_11) ).
fof(c_0_181_182,axiom,
! [X47,X33,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X33,X47,X3)
| ~ c_HOL_Oord__class_Oless(X47,X33,X3) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_182_183,axiom,
! [X39,X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X26,X39,X3)
| ~ c_HOL_Oord__class_Oless(X39,X26,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_183_184,axiom,
! [X39,X26,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X39,X26,X3)
| ~ c_HOL_Oord__class_Oless(X26,X39,X3) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_184_185,axiom,
! [X47,X33,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X47,X33,X3)
| ~ c_HOL_Oord__class_Oless(X33,X47,X3) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_185_186,axiom,
! [X43,X26,X3] :
( c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3) != c_List_Orev(X43,X3)
| X43 = c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3) ),
file('<stdin>',cls_singleton__rev__conv_0) ).
fof(c_0_186_187,axiom,
! [X43,X26,X3] :
( c_List_Orev(X43,X3) != c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3)
| X43 = c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3) ),
file('<stdin>',cls_rev__singleton__conv_0) ).
fof(c_0_187_188,axiom,
! [X39,X26,X17,X8,X3] :
( c_List_Oreplicate(X8,X26,X3) != c_List_Oreplicate(X17,X39,X3)
| X26 = X39
| X8 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_replicate__eq__replicate_1) ).
fof(c_0_188_189,axiom,
! [X39,X26,X17,X8,X3] :
( c_List_Oreplicate(X8,X26,X3) != c_List_Oreplicate(X17,X39,X3)
| X8 = X17 ),
file('<stdin>',cls_replicate__eq__replicate_0) ).
fof(c_0_189_190,axiom,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46)
| X47 = X46 ),
file('<stdin>',cls_add__imp__eq_0) ).
fof(c_0_190_191,axiom,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46)
| X47 = X46 ),
file('<stdin>',cls_add__left__cancel_0) ).
fof(c_0_191_192,axiom,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X33) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X33)
| X47 = X46 ),
file('<stdin>',cls_add__right__cancel_0) ).
fof(c_0_192_193,axiom,
! [X36,X48,X43,X3] :
( c_List_Oappend(X48,X43,X3) != c_List_Oappend(X36,X43,X3)
| X48 = X36 ),
file('<stdin>',cls_append__same__eq_0) ).
fof(c_0_193_194,axiom,
! [X36,X48,X43,X3] :
( c_List_Oappend(X43,X48,X3) != c_List_Oappend(X43,X36,X3)
| X48 = X36 ),
file('<stdin>',cls_same__append__eq_0) ).
fof(c_0_194_195,axiom,
! [X53,X45,X54,X33,X3] :
( c_List_Olist_OCons(X33,X45,X3) != c_List_Olist_OCons(X54,X53,X3)
| X33 = X54 ),
file('<stdin>',cls_list_Oinject_0) ).
fof(c_0_195_196,axiom,
! [X53,X45,X54,X33,X3] :
( c_List_Olist_OCons(X33,X45,X3) != c_List_Olist_OCons(X54,X53,X3)
| X45 = X53 ),
file('<stdin>',cls_list_Oinject_1) ).
fof(c_0_196_197,axiom,
! [X26,X7] :
( c_HOL_Oord__class_Oless(X26,X26,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X26),X7,X26) = c_Lambda_Oliftn(X26,X7,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('<stdin>',cls_substn_Osimps_I1_J_1) ).
fof(c_0_197_198,axiom,
! [X1,X2,X3] :
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X2),X1)) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_198_199,axiom,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X33)))
| X33 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X33))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
file('<stdin>',cls_IT_Ocases_8) ).
fof(c_0_199_200,axiom,
! [X43,X33,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(c_List_Oremove1(X33,X43,X3),X3)
| ~ c_List_Olinorder__class_Osorted(X43,X3) ),
file('<stdin>',cls_sorted__remove1_0) ).
fof(c_0_200_201,axiom,
! [X40,X24,X20] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X24),X40,X20) = c_Lambda_OdB_OVar(X24)
| ~ c_HOL_Oord__class_Oless(X24,X20,tc_nat) ),
file('<stdin>',cls_subst__lt_0) ).
fof(c_0_201_202,axiom,
! [X17,X44,X20] :
( c_Lambda_Oliftn(X17,c_Lambda_OdB_OVar(X20),X44) = c_Lambda_OdB_OVar(X20)
| ~ c_HOL_Oord__class_Oless(X20,X44,tc_nat) ),
file('<stdin>',cls_liftn_Osimps_I1_J_0) ).
fof(c_0_202_203,axiom,
! [X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3),X3) ),
file('<stdin>',cls_sorted_Osimps_I2_J_0) ).
fof(c_0_203_204,axiom,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| hBOOL(hAPP(X31,v_sko__List__XdropWhile__Xinduct__2(X31)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
file('<stdin>',cls_dropWhile_Oinduct_0) ).
fof(c_0_204_205,axiom,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| hBOOL(hAPP(X31,v_sko__List__Xtake__Xinduct__2(X31)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
file('<stdin>',cls_take_Oinduct_0) ).
fof(c_0_205_206,axiom,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| hBOOL(hAPP(X31,v_sko__List__Xconcat__Xinduct__2(X31)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
file('<stdin>',cls_concat_Oinduct_0) ).
fof(c_0_206_207,axiom,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| hBOOL(hAPP(X31,v_sko__List__Xdistinct__Xinduct__2(X31)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
file('<stdin>',cls_distinct_Oinduct_0) ).
fof(c_0_207_208,axiom,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| hBOOL(hAPP(X31,v_sko__List__Xremove1__Xinduct__2(X31)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
file('<stdin>',cls_remove1_Oinduct_0) ).
fof(c_0_208_209,axiom,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| hBOOL(hAPP(X31,v_sko__List__Xlist__Xinduct__2(X31)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
file('<stdin>',cls_list_Oinduct_0) ).
fof(c_0_209_210,axiom,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| hBOOL(hAPP(X31,v_sko__List__Xmap__Xinduct__2(X31)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
file('<stdin>',cls_map_Oinduct_0) ).
fof(c_0_210_211,axiom,
! [X37,X38,X33,X3] :
( hAPP(hAPP(X38,X33),X37) = X33
| ~ c_OrderedGroup_Omonoid__add(X37,X38,X3) ),
file('<stdin>',cls_monoid__add_Oadd__0__right_0) ).
fof(c_0_211_212,axiom,
! [X37,X38,X33,X3] :
( hAPP(hAPP(X38,X37),X33) = X33
| ~ c_OrderedGroup_Omonoid__add(X37,X38,X3) ),
file('<stdin>',cls_monoid__add_Oadd__0__left_0) ).
fof(c_0_212_213,axiom,
! [X15,X20] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X15,X20)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X15)) ),
file('<stdin>',cls_lift__IT_0) ).
fof(c_0_213_214,axiom,
! [X7,X44,X20] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X20),X7,X44) = c_Lambda_OdB_OVar(X20)
| X20 = X44
| c_HOL_Oord__class_Oless(X44,X20,tc_nat) ),
file('<stdin>',cls_substn_Osimps_I1_J_2) ).
fof(c_0_214_215,axiom,
! [X7,X44,X20] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X20),X7,X44) = c_Lambda_OdB_OVar(X20)
| X20 = X44
| c_HOL_Oord__class_Oless(X44,X20,tc_nat) ),
file('<stdin>',cls_subst__Var_2) ).
fof(c_0_215_216,axiom,
! [X43,X3] :
( c_Nat_Osize__class_Osize(c_List_Oremdups(X43,X3),tc_List_Olist(X3)) != c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3))
| c_List_Oremdups(X43,X3) = X43 ),
file('<stdin>',cls_length__remdups__eq_0) ).
fof(c_0_216_217,axiom,
! [X39,X26,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X39,X26,X3)
| c_HOL_Oord__class_Oless(X26,X39,X3)
| X26 = X39 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_217_218,axiom,
! [X39,X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| X26 = X39
| c_HOL_Oord__class_Oless(X39,X26,X3)
| c_HOL_Oord__class_Oless(X26,X39,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_218_219,axiom,
! [X39,X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X39,X26,X3)
| c_HOL_Oord__class_Oless(X26,X39,X3)
| X26 = X39 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_219_220,axiom,
! [X39,X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X39,X26,X3)
| X26 = X39
| c_HOL_Oord__class_Oless(X26,X39,X3) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_220_221,axiom,
! [X39,X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| X26 = X39
| c_HOL_Oord__class_Oless(X26,X39,X3)
| c_HOL_Oord__class_Oless(X39,X26,X3) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_221_222,axiom,
! [X65,X66,X67,X68] :
( hAPP(hAPP(c_Type_Otype_OFun,X68),X66) != hAPP(hAPP(c_Type_Otype_OFun,X67),X65)
| X66 = X65 ),
file('<stdin>',cls_type_Osimps_I2_J_1) ).
fof(c_0_222_223,axiom,
! [X65,X66,X67,X68] :
( hAPP(hAPP(c_Type_Otype_OFun,X68),X66) != hAPP(hAPP(c_Type_Otype_OFun,X67),X65)
| X68 = X67 ),
file('<stdin>',cls_type_Osimps_I2_J_0) ).
fof(c_0_223_224,axiom,
! [X11,X12,X13,X14] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X14),X12) != hAPP(hAPP(c_Lambda_OdB_OApp,X13),X11)
| X14 = X13 ),
file('<stdin>',cls_dB_Osimps_I2_J_0) ).
fof(c_0_224_225,axiom,
! [X11,X12,X13,X14] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X14),X12) != hAPP(hAPP(c_Lambda_OdB_OApp,X13),X11)
| X12 = X11 ),
file('<stdin>',cls_dB_Osimps_I2_J_1) ).
fof(c_0_225_226,axiom,
! [X26,X7] :
( c_HOL_Oord__class_Oless(X26,X26,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X26),X7,X26) = X7 ),
file('<stdin>',cls_subst__Var_1) ).
fof(c_0_226_227,axiom,
! [X46,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X33) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_227_228,axiom,
! [X47,X33,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X33) ),
file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).
fof(c_0_228_229,axiom,
! [X39,X26,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X39) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X39),X26) ),
file('<stdin>',cls_class__semiring_Oadd__c_0) ).
fof(c_0_229_230,axiom,
! [X20,X21,X23] :
( hAPP(X21,X20) = X23
| ~ c_Type_Otyping(X21,c_Lambda_OdB_OVar(X20),X23) ),
file('<stdin>',cls_typing__elims_I1_J_0) ).
fof(c_0_230_231,axiom,
! [X17,X8] :
( c_HOL_Oord__class_Oless(X17,X8,tc_nat)
| c_HOL_Oord__class_Oless(X8,X17,tc_nat)
| X8 = X17 ),
file('<stdin>',cls_nat__neq__iff_0) ).
fof(c_0_231_232,axiom,
! [X39,X26] :
( c_HOL_Oord__class_Oless(X39,X26,tc_nat)
| c_HOL_Oord__class_Oless(X26,X39,tc_nat)
| X26 = X39 ),
file('<stdin>',cls_linorder__neqE__nat_0) ).
fof(c_0_232_233,axiom,
! [X44,X20] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X20),X44) = c_Lambda_OdB_OVar(X20)
| ~ c_HOL_Oord__class_Oless(X20,X44,tc_nat) ),
file('<stdin>',cls_lift_Osimps_I1_J_0) ).
fof(c_0_233_234,axiom,
! [X26,X33,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X26 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X33)
| X33 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).
fof(c_0_234_235,axiom,
! [X33,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33) != c_HOL_Ozero__class_Ozero(X3)
| X33 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_double__eq__0__iff_0) ).
fof(c_0_235_236,axiom,
! [X43,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3)),tc_nat)
| X43 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_length__greater__0__conv_1) ).
fof(c_0_236_237,axiom,
! [X43,X17,X3] :
( c_List_Orotate(X17,X43,X3) != c_List_Olist_ONil(X3)
| X43 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_rotate__is__Nil__conv_0) ).
fof(c_0_237_238,axiom,
! [X48,X43,X3] :
( c_List_Oappend(X43,X48,X3) != c_List_Olist_ONil(X3)
| X48 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_append__is__Nil__conv_1) ).
fof(c_0_238_239,axiom,
! [X48,X43,X3] :
( c_List_Oappend(X43,X48,X3) != c_List_Olist_ONil(X3)
| X43 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_append__is__Nil__conv_0) ).
fof(c_0_239_240,axiom,
! [X48,X43,X3] :
( c_List_Olist_ONil(X3) != c_List_Oappend(X43,X48,X3)
| X48 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_Nil__is__append__conv_1) ).
fof(c_0_240_241,axiom,
! [X48,X43,X3] :
( c_List_Olist_ONil(X3) != c_List_Oappend(X43,X48,X3)
| X43 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_Nil__is__append__conv_0) ).
fof(c_0_241_242,axiom,
! [X26,X17,X3] :
( c_List_Oreplicate(X17,X26,X3) != c_List_Olist_ONil(X3)
| X17 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_replicate__empty_0) ).
fof(c_0_242_243,axiom,
! [X26,X17,X3] :
( c_List_Olist_ONil(X3) != c_List_Oreplicate(X17,X26,X3)
| X17 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_empty__replicate_0) ).
fof(c_0_243_244,axiom,
! [X26,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X26,X26,X3) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_244_245,axiom,
! [X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X26,X26,X3) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_245_246,axiom,
! [X26,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X26,X26,X3) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_246_247,axiom,
! [X48,X43,X3] :
( X48 != c_List_Oappend(X43,X48,X3)
| X43 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_self__append__conv2_0) ).
fof(c_0_247_248,axiom,
! [X48,X43,X3] :
( c_List_Oappend(X43,X48,X3) != X48
| X43 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_append__self__conv2_0) ).
fof(c_0_248_249,axiom,
! [X48,X43,X3] :
( X43 != c_List_Oappend(X43,X48,X3)
| X48 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_self__append__conv_0) ).
fof(c_0_249_250,axiom,
! [X48,X43,X3] :
( c_List_Oappend(X43,X48,X3) != X43
| X48 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_append__self__conv_0) ).
fof(c_0_250_251,axiom,
! [X43,X3] :
( c_List_Oremdups(X43,X3) != X43
| c_Nat_Osize__class_Osize(c_List_Oremdups(X43,X3),tc_List_Olist(X3)) = c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3)) ),
file('<stdin>',cls_length__remdups__eq_1) ).
fof(c_0_251_252,axiom,
! [X10] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X10)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X10)) ),
file('<stdin>',cls_Lambda_0) ).
fof(c_0_252_253,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_double__eq__0__iff_1) ).
fof(c_0_253_254,axiom,
! [X26,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X26 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),c_HOL_Ozero__class_Ozero(X3)) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).
fof(c_0_254_255,axiom,
! [X26,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X26) = X26 ),
file('<stdin>',cls_class__semiring_Oadd__0_0) ).
fof(c_0_255_256,axiom,
! [X33,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X33) = X33 ),
file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).
fof(c_0_256_257,axiom,
! [X33,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X33) = X33 ),
file('<stdin>',cls_add__0__left_0) ).
fof(c_0_257_258,axiom,
! [X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X33) = X33 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_258_259,axiom,
! [X49,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(c_List_Oremdups(X49,X3),X3)
| ~ c_List_Olinorder__class_Osorted(X49,X3) ),
file('<stdin>',cls_sorted__remdups_0) ).
fof(c_0_259_260,axiom,
! [X33,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Ozero__class_Ozero(X3)) = X33 ),
file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).
fof(c_0_260_261,axiom,
! [X33,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Ozero__class_Ozero(X3)) = X33 ),
file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).
fof(c_0_261_262,axiom,
! [X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Ozero__class_Ozero(X3)) = X33 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_262_263,axiom,
! [X17] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
| X17 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_gr0I_0) ).
fof(c_0_263_264,axiom,
! [X48,X43,X3] :
( c_List_Orev(X43,X3) != c_List_Orev(X48,X3)
| X43 = X48 ),
file('<stdin>',cls_rev__is__rev__conv_0) ).
fof(c_0_264_265,axiom,
! [X43,X3] :
( c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3)) != c_HOL_Ozero__class_Ozero(tc_nat)
| X43 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_length__0__conv_0) ).
fof(c_0_265_266,axiom,
! [X4,X5] :
( class_Orderings_Opreorder(tc_fun(X4,X5))
| ~ class_Orderings_Opreorder(X5) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_266_267,axiom,
! [X4,X5] :
( class_Orderings_Oorder(tc_fun(X4,X5))
| ~ class_Orderings_Oorder(X5) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_267_268,axiom,
! [X26,X3] :
( c_List_Oremdups(X26,X3) != c_List_Olist_ONil(X3)
| X26 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_remdups__eq__nil__iff_0) ).
fof(c_0_268_269,axiom,
! [X43,X3] :
( c_List_Olist_ONil(X3) != c_List_Orev(X43,X3)
| X43 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_Nil__is__rev__conv_0) ).
fof(c_0_269_270,axiom,
! [X26,X3] :
( c_List_Olist_ONil(X3) != c_List_Oremdups(X26,X3)
| X26 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_remdups__eq__nil__right__iff_0) ).
fof(c_0_270_271,axiom,
! [X43,X3] :
( c_List_Orev(X43,X3) != c_List_Olist_ONil(X3)
| X43 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_rev__is__Nil__conv_0) ).
fof(c_0_271_272,axiom,
! [X3] :
( ~ class_OrderedGroup_Osemigroup__add(X3)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X3),X3) ),
file('<stdin>',cls_semigroup__add__class_Oaxioms_0) ).
fof(c_0_272_273,axiom,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(c_List_Olist_ONil(X3),X3) ),
file('<stdin>',cls_sorted_Osimps_I1_J_0) ).
fof(c_0_273_274,axiom,
! [X57,X55] :
( c_Lambda_OdB_OAbs(X55) != c_Lambda_OdB_OAbs(X57)
| X55 = X57 ),
file('<stdin>',cls_dB_Osimps_I3_J_0) ).
fof(c_0_274_275,axiom,
! [X18,X19] :
( c_Lambda_OdB_OVar(X19) != c_Lambda_OdB_OVar(X18)
| X19 = X18 ),
file('<stdin>',cls_dB_Osimps_I1_J_0) ).
fof(c_0_275_276,plain,
! [X34,X9,X20,X21,X22,X35,X23] :
( X22 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X23,X22,X21,X34),X23,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X22)
| ~ c_Type_Otypings(X21,X9,X35)
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X34,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_276_277,plain,
! [X27,X16,X17] :
( X27 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X17,X16,X27),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X16,tc_Lambda_OdB,tc_Lambda_OdB)),X27)) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_277_278,plain,
! [X34,X9,X20,X21,X22,X35,X23] :
( c_Type_Otypings(X21,X34,c_Type_Osko__Type__Xvar__app__types__1__1(X23,X22,X21,X34))
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X22)
| ~ c_Type_Otypings(X21,X9,X35)
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X34,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_278_279,plain,
! [X27,X16,X17] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X16,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X17,X16,X27),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X16,tc_Lambda_OdB,tc_Lambda_OdB)),X27)) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_279_280,plain,
! [X15,X31] :
( ~ hBOOL(hAPP(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X31)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X31),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X31)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X31),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(X31,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_280_281,plain,
! [X15,X31] :
( hBOOL(hAPP(X31,X15))
| ~ hBOOL(hAPP(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X31)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X31),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X31)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X31),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_281_282,plain,
! [X6,X16,X10] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X16,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X6,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X16,X6,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_282_283,plain,
! [X6,X7,X10] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X6,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_283_284,plain,
! [X6,X7,X10] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X6,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_284_285,plain,
! [X6,X7,X10] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10)),X7),X6,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X10,X7,c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_285_286,plain,
! [X45,X29,X30,X33,X31] :
( ~ hBOOL(hAPP(X31,c_List_Olist_Olist__case(X30,X29,c_List_Olist_OCons(X33,X45,t_b),t_a,t_b)))
| hBOOL(hAPP(X31,hAPP(hAPP(X29,X33),X45))) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_286_287,plain,
! [X42,X25,X29,X30,X31] :
( ~ hBOOL(hAPP(X31,c_List_Olist_Olist__case(X30,X29,c_List_Olist_OCons(X25,X42,t_b),t_a,t_b)))
| hBOOL(hAPP(X31,hAPP(hAPP(X29,X25),X42))) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_287_288,plain,
! [X41,X42,X28,X29,X30,X31] :
( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X30,X29,X28,hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41),t_a)))
| hBOOL(hAPP(X31,hAPP(hAPP(X29,X42),X41))) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_288_289,plain,
! [X28,X29,X30,X12,X14,X31] :
( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X30,X29,X28,hAPP(hAPP(c_Lambda_OdB_OApp,X14),X12),t_a)))
| hBOOL(hAPP(X31,hAPP(hAPP(X29,X14),X12))) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_289_290,plain,
! [X15,X31] :
( hBOOL(hAPP(X31,c_ListApplication_Osko__ListApplication__Xlem__1__3(X31)))
| ~ hBOOL(hAPP(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X31)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X31),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(X31,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_290_291,plain,
! [X15,X31] :
( hBOOL(hAPP(X31,X15))
| hBOOL(hAPP(X31,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X31)))
| ~ hBOOL(hAPP(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X31)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X31),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_291_292,plain,
! [X9,X20,X21,X22,X23] :
( X23 = X22
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X22)
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_292_293,plain,
! [X28,X29,X30,X55,X31] :
( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X30,X29,X28,c_Lambda_OdB_OAbs(X55),t_a)))
| hBOOL(hAPP(X31,hAPP(X28,X55))) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_293_294,plain,
! [X25,X28,X29,X30,X31] :
( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X30,X29,X28,c_Lambda_OdB_OAbs(X25),t_a)))
| hBOOL(hAPP(X31,hAPP(X28,X25))) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_294_295,plain,
! [X32,X28,X29,X30,X31] :
( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X30,X29,X28,c_Lambda_OdB_OVar(X32),t_a)))
| hBOOL(hAPP(X31,hAPP(X30,X32))) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_295_296,plain,
! [X19,X28,X29,X30,X31] :
( ~ hBOOL(hAPP(X31,c_Lambda_OdB_OdB__case(X30,X29,X28,c_Lambda_OdB_OVar(X19),t_a)))
| hBOOL(hAPP(X31,hAPP(X30,X19))) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_296_297,plain,
! [X29,X30,X31] :
( ~ hBOOL(hAPP(X31,c_List_Olist_Olist__case(X30,X29,c_List_Olist_ONil(t_b),t_a,t_b)))
| hBOOL(hAPP(X31,X30)) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_297_298,plain,
! [X6,X7,X10] :
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X10,X7,c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X7,tc_Lambda_OdB)
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10)),X7),X6,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_298_299,plain,
! [X9,X20,X21,X23] :
( c_Type_Otyping(X21,c_Lambda_OdB_OVar(X20),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X23,X21,X20,X9),X23,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_299_300,plain,
! [X9,X15,X21,X23] :
( c_Type_Otyping(X21,X15,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X23,X21,X15,X9),X23,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X9,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_300_301,plain,
! [X9,X15,X21,X23] :
( c_Type_Otyping(X21,X15,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X23,X21,X15,X9),X23,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X9,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_301_302,plain,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X33),v_sko__InductTermi__XIT__Xcases__5(X33),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X33)))
| X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X33)),v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_302_303,plain,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X33),v_sko__InductTermi__XIT__Xcases__5(X33),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)))
| X33 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X33))
| X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X33)),v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_303_304,axiom,
! [X26,X15,X7] :
( c_List_Oappend(X26,c_List_Olist_OCons(X7,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X26,tc_Lambda_OdB,tc_Lambda_OdB)),X7) = c_List_Ofoldl(c_Lambda_OdB_OApp,X15,c_List_Oappend(X26,c_List_Olist_OCons(X7,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_28 ).
fof(c_0_304_305,plain,
! [X9,X15,X21,X35,X23] :
( c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X9,tc_Lambda_OdB,tc_Lambda_OdB),X23)
| ~ c_Type_Otypings(X21,X9,X35)
| ~ c_Type_Otyping(X21,X15,c_List_Ofoldr(c_Type_Otype_OFun,X35,X23,tc_Type_Otype,tc_Type_Otype)) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_305_306,plain,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X33),v_sko__InductTermi__XIT__Xcases__5(X33),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X33)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_306_307,plain,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X33),v_sko__InductTermi__XIT__Xcases__5(X33),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)))
| X33 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X33))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_307_308,plain,
! [X16,X17] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X16,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X16,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_308_309,plain,
! [X9,X20,X21,X23] :
( c_Type_Otypings(X21,X9,c_Type_Osko__Type__Xvar__app__typesE__1__1(X23,X21,X20,X9))
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X9,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_309_310,plain,
! [X9,X15,X21,X23] :
( c_Type_Otypings(X21,X9,c_Type_Osko__Type__Xlist__app__typeD__1__1(X23,X21,X15,X9))
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X9,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_310_311,plain,
! [X9,X15,X21,X23] :
( c_Type_Otypings(X21,X9,c_Type_Osko__Type__Xlist__app__typeE__1__1(X23,X21,X15,X9))
| ~ c_Type_Otyping(X21,c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X9,tc_Lambda_OdB,tc_Lambda_OdB),X23) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_311_312,axiom,
! [X6,X7,X16,X10] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),X16,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X10 = X7 ),
c_0_36 ).
fof(c_0_312_313,axiom,
! [X6,X7,X16,X10] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),X16,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X7),X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X16 = X6 ),
c_0_37 ).
fof(c_0_313_314,axiom,
! [X6,X16,X17,X8] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X16,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X8 = X17 ),
c_0_38 ).
fof(c_0_314_315,axiom,
! [X6,X16,X17,X8] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X16,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X17),X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X16 = X6 ),
c_0_39 ).
fof(c_0_315_316,plain,
! [X36,X39,X26,X3] :
( ~ class_OrderedGroup_Osemigroup__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X39),X36,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X39,X36,X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_316_317,axiom,
! [X9,X7,X10] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X9,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X9,tc_Lambda_OdB,tc_Lambda_OdB)
| X10 = X7 ),
c_0_41 ).
fof(c_0_317_318,plain,
! [X36,X39,X26,X38,X3] :
( c_List_Ofoldl(X38,hAPP(hAPP(X38,X26),X39),X36,X3,X3) = hAPP(hAPP(X38,X26),c_List_Ofoldl(X38,X39,X36,X3,X3))
| ~ c_OrderedGroup_Osemigroup__add(X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_318_319,plain,
! [X36,X37,X26,X38,X3] :
( hAPP(hAPP(X38,X26),c_List_Ofoldl(X38,X37,X36,X3,X3)) = c_List_Ofoldl(X38,X26,X36,X3,X3)
| ~ c_OrderedGroup_Omonoid__add(X37,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_319_320,plain,
! [X43,X33,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X33,X43,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X43,c_HOL_Ozero__class_Ozero(X3),X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_320_321,plain,
! [X36,X26,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X36,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X26,X36,X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_321_322,axiom,
! [X9,X15,X7,X10] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X10),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X9,tc_Lambda_OdB,tc_Lambda_OdB)
| X10 = c_List_Ofoldl(c_Lambda_OdB_OApp,X15,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X10,X7,X15,X9),tc_Lambda_OdB,tc_Lambda_OdB)
| X9 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_46 ).
fof(c_0_322_323,axiom,
! [X25,X7,X10] :
( X10 != c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X10),X7),X25,tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X10),X7) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X10),X7),c_List_Oappend(X25,c_List_Olist_OCons(X7,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_47 ).
fof(c_0_323_324,plain,
! [X33] :
( X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X33))),v_sko__InductTermi__XIT__Xcases__5(X33)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X33)))
| X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X33)),v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_324_325,plain,
! [X33] :
( X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X33))),v_sko__InductTermi__XIT__Xcases__5(X33)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| X33 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X33))
| X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X33)),v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_325_326,axiom,
! [X9,X15,X7,X10] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X10),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X15,X9,tc_Lambda_OdB,tc_Lambda_OdB)
| X9 = c_List_Oappend(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X10,X7,X15,X9),c_List_Olist_OCons(X7,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)
| X9 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_50 ).
fof(c_0_326_327,axiom,
! [X36,X48,X43,X8,X63,X3] :
( c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3)) != c_Nat_Osize__class_Osize(X48,tc_List_Olist(X63))
| c_Map_Omap__upds(X8,c_List_Oappend(X43,X36,X3),X48,X3,X63) = c_Map_Omap__upds(X8,X43,X48,X3,X63) ),
c_0_51 ).
fof(c_0_327_328,axiom,
! [X36,X48,X43,X8,X63,X3] :
( c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3)) != c_Nat_Osize__class_Osize(X48,tc_List_Olist(X63))
| c_Map_Omap__upds(X8,X43,c_List_Oappend(X48,X36,X63),X3,X63) = c_Map_Omap__upds(X8,X43,X48,X3,X63) ),
c_0_52 ).
fof(c_0_328_329,plain,
! [X43,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X43,X3,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X43,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_329_330,plain,
! [X43,X33,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X43,X33,X3,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X33,X43,X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_330_331,axiom,
! [X15,X7,X10] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X10),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X15,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X10),X7) = X15 ),
c_0_55 ).
fof(c_0_331_332,axiom,
! [X6,X7,X10] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X10)
| X7 = c_Lambda_OdB_OAbs(X10) ),
c_0_56 ).
fof(c_0_332_333,axiom,
! [X6,X7,X10] :
( c_Lambda_OdB_OAbs(X10) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X10) = X7 ),
c_0_57 ).
fof(c_0_333_334,axiom,
! [X6,X7,X8] :
( c_Lambda_OdB_OVar(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X8) = X7 ),
c_0_58 ).
fof(c_0_334_335,axiom,
! [X6,X7,X10] :
( c_Lambda_OdB_OAbs(X10) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X6 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_59 ).
fof(c_0_335_336,axiom,
! [X6,X7,X10] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X10)
| X6 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_60 ).
fof(c_0_336_337,axiom,
! [X6,X7,X8] :
( c_Lambda_OdB_OVar(X8) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X6,tc_Lambda_OdB,tc_Lambda_OdB)
| X6 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_61 ).
fof(c_0_337_338,plain,
! [X39,X26,X10,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X39),X26))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X10,X3,X3),X3),X26),X39)) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_338_339,plain,
! [X48,X39,X43,X26,X10,X3] :
( hBOOL(hAPP(hAPP(X10,X39),X26))
| c_ListOrder_Ostep1(X10,X48,X43,X3)
| ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X48,c_List_Olist_OCons(X39,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_339_340,plain,
! [X48,X39,X43,X26,X10,X3] :
( X48 = X43
| c_ListOrder_Ostep1(X10,X48,X43,X3)
| ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X48,c_List_Olist_OCons(X39,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_340_341,plain,
! [X48,X39,X43,X26,X10,X3] :
( hBOOL(hAPP(hAPP(X10,X39),X26))
| X39 = X26
| ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X48,c_List_Olist_OCons(X39,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_341_342,plain,
! [X33] :
( X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X33))),v_sko__InductTermi__XIT__Xcases__5(X33)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X33)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_342_343,axiom,
! [X43,X50,X26,X51,X20,X3] :
( c_List_Olist__update(c_List_Olist__update(X43,X20,X26,X3),X51,X50,X3) = c_List_Olist__update(c_List_Olist__update(X43,X51,X50,X3),X20,X26,X3)
| X20 = X51 ),
c_0_67 ).
fof(c_0_343_344,plain,
! [X48,X39,X43,X26,X10,X3] :
( X48 = X43
| X39 = X26
| ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X48,c_List_Olist_OCons(X39,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X43,c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_344_345,plain,
! [X33] :
( X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X33))),v_sko__InductTermi__XIT__Xcases__5(X33)),v_sko__InductTermi__XIT__Xcases__6(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| X33 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X33))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_345_346,plain,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X33)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X33)))
| X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X33)),v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_346_347,plain,
! [X39,X26,X10,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X10,X3,X3),X3),X26),X39))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X39),X26)) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_347_348,plain,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X33)))
| X33 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X33))
| X33 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X33)),v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_348_349,plain,
! [X9,X15,X21,X35] :
( c_Type_Otypings(X21,X9,c_Type_Osko__Type__Xtypes__snocE__1__1(X35,X21,X15,X9))
| ~ c_Type_Otypings(X21,c_List_Oappend(X9,c_List_Olist_OCons(X15,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X35) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_349_350,plain,
! [X9,X15,X21,X35] :
( c_Type_Otyping(X21,X15,c_Type_Osko__Type__Xtypes__snocE__1__2(X35,X21,X15,X9))
| ~ c_Type_Otypings(X21,c_List_Oappend(X9,c_List_Olist_OCons(X15,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X35) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_350_351,plain,
! [X52,X15,X59,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X15)),hAPP(hAPP(c_Lambda_OdB_OApp,X59),X52)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X15),X52))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X59)) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_351_352,plain,
! [X15,X7,X10,X20] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X10,X15,X20)),c_Lambda_Osubst(X7,X15,X20)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_352_353,plain,
! [X15,X7,X10,X20] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X15,X10,X20)),c_Lambda_Osubst(X15,X7,X20)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_353_354,plain,
! [X48,X39,X43,X26,X10,X3] :
( c_ListOrder_Ostep1(X10,X48,X43,X3)
| hBOOL(hAPP(hAPP(X10,X39),X26))
| ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X39,X48,X3),c_List_Olist_OCons(X26,X43,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_354_355,plain,
! [X48,X43,X26,X17,X3] :
( c_List_Olist__update(c_List_Oappend(X43,X48,X3),X17,X26,X3) = c_List_Oappend(c_List_Olist__update(X43,X17,X26,X3),X48,X3)
| ~ c_HOL_Oord__class_Oless(X17,c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_355_356,plain,
! [X48,X43,X26,X20,X3] :
( c_List_Olist__update(c_List_Oappend(X43,X48,X3),X20,X26,X3) = c_List_Oappend(c_List_Olist__update(X43,X20,X26,X3),X48,X3)
| ~ c_HOL_Oord__class_Oless(X20,c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3)),tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_356_357,plain,
! [X48,X39,X43,X26,X10,X3] :
( c_List_Olistrelp(X10,c_List_Olist_OCons(X26,X43,X3),c_List_Olist_OCons(X39,X48,X3),X3)
| ~ c_List_Olistrelp(X10,X43,X48,X3)
| ~ hBOOL(hAPP(hAPP(X10,X26),X39)) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_357_358,plain,
! [X48,X39,X43,X26,X10,X3] :
( c_ListOrder_Ostep1(X10,X48,X43,X3)
| X43 = X48
| ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X39,X48,X3),c_List_Olist_OCons(X26,X43,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_358_359,plain,
! [X15,X7,X10,X20] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X15,X10,X20)),c_Lambda_Osubst(X15,X7,X20)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_359_360,plain,
! [X10,X47,X33,X63,X3] :
( hBOOL(hAPP(hAPP(X10,X47),X33))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X3,X63),X33),X47)) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_360_361,plain,
! [X10,X69,X70,X63,X3] :
( hBOOL(hAPP(hAPP(X10,X69),X70))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X3,X63),X70),X69)) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_361_362,plain,
! [X48,X43,X26,X10,X3] :
( ~ c_ListOrder_Ostep1(X10,X48,X43,X3)
| c_ListOrder_Ostep1(X10,c_List_Oappend(X48,X26,X3),c_List_Oappend(X43,X26,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_362_363,plain,
! [X26,X60,X34,X10,X3] :
( c_ListOrder_Ostep1(X10,c_List_Oappend(X26,X60,X3),c_List_Oappend(X26,X34,X3),X3)
| ~ c_ListOrder_Ostep1(X10,X60,X34,X3) ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_363_364,plain,
! [X48,X43,X26,X10,X3] :
( c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X26,X48,X3),c_List_Olist_OCons(X26,X43,X3),X3)
| ~ c_ListOrder_Ostep1(X10,X48,X43,X3) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_364_365,plain,
! [X15,X59,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X15)),hAPP(hAPP(c_Lambda_OdB_OApp,X59),X15)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X59)) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_365_366,plain,
! [X52,X15,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X15)),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X52)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X15),X52)) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_366_367,plain,
! [X15,X7,X10,X20] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X10,X15,X20)),c_Lambda_Osubst(X7,X15,X20)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_367_368,plain,
! [X42,X25,X26,X31,X3] :
( ~ hBOOL(hAPP(X31,X26))
| hBOOL(hAPP(X31,c_List_Osko__List__XCons__eq__filter__iff__1__3(X31,X25,X3)))
| c_List_Olist_OCons(X26,c_List_Ofilter(X31,X42,X3),X3) = c_List_Ofilter(X31,c_List_Oappend(X25,c_List_Olist_OCons(X26,X42,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_368_369,plain,
! [X42,X25,X26,X31,X3] :
( ~ hBOOL(hAPP(X31,X26))
| hBOOL(hAPP(X31,c_List_Osko__List__Xfilter__eq__Cons__iff__1__3(X31,X25,X3)))
| c_List_Ofilter(X31,c_List_Oappend(X25,c_List_Olist_OCons(X26,X42,X3),X3),X3) = c_List_Olist_OCons(X26,c_List_Ofilter(X31,X42,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_369_370,axiom,
! [X48,X43,X62,X63,X3] :
( c_List_Omap(X62,X43,X63,X3) != c_List_Omap(X62,X48,X63,X3)
| c_Nat_Osize__class_Osize(X43,tc_List_Olist(X63)) = c_Nat_Osize__class_Osize(X48,tc_List_Olist(X63)) ),
c_0_94 ).
fof(c_0_370_371,plain,
! [X48,X39,X43,X26,X10,X3] :
( X26 = X39
| hBOOL(hAPP(hAPP(X10,X39),X26))
| ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X39,X48,X3),c_List_Olist_OCons(X26,X43,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_371_372,plain,
! [X58,X39,X26,X10,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X26),X58))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X39),X58))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X26),X39)) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_372_373,plain,
! [X48,X39,X43,X26,X10,X3] :
( X26 = X39
| X43 = X48
| ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X39,X48,X3),c_List_Olist_OCons(X26,X43,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_373_374,plain,
! [X61,X46,X47,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X61)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X61)) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_374_375,plain,
! [X36,X39,X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X39,X36,X3),X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X26,c_List_Olist_OCons(X39,X36,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_375_376,plain,
! [X10,X47,X33,X63,X3] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X3,X63),X33),X47))
| ~ hBOOL(hAPP(hAPP(X10,X47),X33)) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_376_377,plain,
! [X10,X47,X33,X63,X3] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X3,X63),X47),X33))
| ~ hBOOL(hAPP(hAPP(X10,X33),X47)) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_377_378,plain,
! [X40,X15,X7] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X40),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X40),X15)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X15)) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_378_379,plain,
! [X40,X15,X7] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X40)),hAPP(hAPP(c_Lambda_OdB_OApp,X15),X40)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X15)) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_379_380,plain,
! [X10,X46,X47,X33,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X33),X46))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X47),X46))
| ~ hBOOL(hAPP(hAPP(X10,X33),X47)) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_380_381,plain,
! [X10,X46,X47,X33,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X33),X46))
| ~ hBOOL(hAPP(hAPP(X10,X47),X46))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X33),X47)) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_381_382,plain,
! [X39,X25,X26,X10,X3] :
( ~ hBOOL(hAPP(hAPP(X10,X39),X25))
| c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X39,X26,X3),c_List_Olist_OCons(X25,X26,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_382_383,plain,
! [X7,X10,X20] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X10,X20)),c_Lambda_Olift(X7,X20)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_383_384,axiom,
! [X48,X39,X43,X26,X3] :
( c_List_Oappend(X43,c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X48,c_List_Olist_OCons(X39,c_List_Olist_ONil(X3),X3),X3)
| X43 = X48 ),
c_0_108 ).
fof(c_0_384_385,axiom,
! [X48,X39,X43,X26,X3] :
( c_List_Oappend(X43,c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X48,c_List_Olist_OCons(X39,c_List_Olist_ONil(X3),X3),X3)
| X26 = X39 ),
c_0_109 ).
fof(c_0_385_386,plain,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| ~ hBOOL(hAPP(X31,c_List_Olist_OCons(v_sko__List__Xconcat__Xinduct__1(X31),v_sko__List__Xconcat__Xinduct__2(X31),t_a)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_386_387,plain,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| ~ hBOOL(hAPP(X31,c_List_Olist_OCons(v_sko__List__Xtake__Xinduct__1(X31),v_sko__List__Xtake__Xinduct__2(X31),t_a)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_387_388,plain,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| ~ hBOOL(hAPP(X31,c_List_Olist_OCons(v_sko__List__Xmap__Xinduct__1(X31),v_sko__List__Xmap__Xinduct__2(X31),t_a)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_388_389,plain,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| ~ hBOOL(hAPP(X31,c_List_Olist_OCons(v_sko__List__Xlist__Xinduct__1(X31),v_sko__List__Xlist__Xinduct__2(X31),t_a)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_389_390,plain,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| ~ hBOOL(hAPP(X31,c_List_Olist_OCons(v_sko__List__XdropWhile__Xinduct__1(X31),v_sko__List__XdropWhile__Xinduct__2(X31),t_a)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_390_391,plain,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| ~ hBOOL(hAPP(X31,c_List_Olist_OCons(v_sko__List__Xremove1__Xinduct__1(X31),v_sko__List__Xremove1__Xinduct__2(X31),t_a)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_391_392,plain,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| ~ hBOOL(hAPP(X31,c_List_Olist_OCons(v_sko__List__Xdistinct__Xinduct__1(X31),v_sko__List__Xdistinct__Xinduct__2(X31),t_a)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_392_393,plain,
! [X46,X47,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47)),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46)),X47) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_393_394,plain,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X33,X47,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X46),X3) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_394_395,plain,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X33,X47,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X47),X3) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_395_396,plain,
! [X59,X7] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X7)),c_Lambda_OdB_OAbs(X59)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X59)) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_396_397,plain,
! [X61,X46,X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X61),X3)
| ~ c_HOL_Oord__class_Oless(X46,X61,X3)
| ~ c_HOL_Oord__class_Oless(X33,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_397_398,plain,
! [X10,X47,X33,X3] :
( c_Wellfounded_Oaccp(X10,X47,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X47),X33))
| ~ c_Wellfounded_Oaccp(X10,X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_398_399,plain,
! [X10,X47,X33,X3] :
( c_Wellfounded_Oaccp(X10,X47,X3)
| ~ c_Wellfounded_Oaccp(X10,X33,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X47),X33)) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_399_400,plain,
! [X46,X47,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47)),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X46)) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_400_401,plain,
! [X61,X46,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X61)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46)),X61) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_401_402,plain,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47)),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X46)) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_402_403,plain,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47)),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X46)) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_403_404,plain,
! [X58,X39,X26,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X39),X58)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X39)),X58) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_404_405,plain,
! [X15,X7,X64,X22,X23] :
( c_Type_Otyping(X64,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X15),X22)
| ~ c_Type_Otyping(X64,X15,X23)
| ~ c_Type_Otyping(X64,X7,hAPP(hAPP(c_Type_Otype_OFun,X23),X22)) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_405_406,axiom,
! [X43,X62,X63,X3] :
( c_List_Omap(X62,X43,X63,X3) != c_List_Olist_ONil(X3)
| X43 = c_List_Olist_ONil(X63) ),
c_0_130 ).
fof(c_0_406_407,axiom,
! [X43,X62,X63,X3] :
( c_List_Olist_ONil(X3) != c_List_Omap(X62,X43,X63,X3)
| X43 = c_List_Olist_ONil(X63) ),
c_0_131 ).
fof(c_0_407_408,axiom,
! [X43,X26,X44,X3] :
( c_List_Olist__update(X43,X44,X26,X3) != c_List_Olist_ONil(X3)
| X43 = c_List_Olist_ONil(X3) ),
c_0_132 ).
fof(c_0_408_409,plain,
! [X52,X15,X21,X23] :
( c_Type_Otyping(X21,X52,X23)
| ~ c_Type_Otyping(X21,X15,X23)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X15),X52)) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_409_410,plain,
! [X58,X39,X26,X40,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X39),X58)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X39),X40)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X58) = X40 ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_410_411,plain,
! [X43,X26,X31,X3] :
( c_List_Ofilter(X31,c_List_Olist_OCons(X26,X43,X3),X3) = c_List_Olist_OCons(X26,c_List_Ofilter(X31,X43,X3),X3)
| ~ hBOOL(hAPP(X31,X26)) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_411_412,plain,
! [X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X47,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_412_413,plain,
! [X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X47,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_413_414,plain,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X46),X3)
| ~ c_HOL_Oord__class_Oless(X33,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_414_415,plain,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X46),X3)
| ~ c_HOL_Oord__class_Oless(X33,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_415_416,plain,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X47),X3)
| ~ c_HOL_Oord__class_Oless(X33,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_416_417,plain,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X47),X3)
| ~ c_HOL_Oord__class_Oless(X33,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_417_418,plain,
! [X7,X10,X20] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X10,X20)),c_Lambda_Olift(X7,X20)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_418_419,plain,
! [X46,X47,X33,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X47,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46),X3)
| ~ c_HOL_Oord__class_Oless(X47,X46,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_419_420,plain,
! [X38,X46,X47,X33,X3] :
( hAPP(hAPP(X38,hAPP(hAPP(X38,X33),X47)),X46) = hAPP(hAPP(X38,X33),hAPP(hAPP(X38,X47),X46))
| ~ c_OrderedGroup_Osemigroup__add(X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_420_421,plain,
! [X48,X43,X56,X3] :
( c_List_Olistsp(X56,c_List_Oappend(X43,X48,X3),X3)
| ~ c_List_Olistsp(X56,X48,X3)
| ~ c_List_Olistsp(X56,X43,X3) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_421_422,axiom,
! [X39,X43,X26,X3] :
( c_List_Oremove1(X26,c_List_Olist_OCons(X39,X43,X3),X3) = c_List_Olist_OCons(X39,c_List_Oremove1(X26,X43,X3),X3)
| X26 = X39 ),
c_0_146 ).
fof(c_0_422_423,plain,
! [X33,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),X3) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_423_424,plain,
! [X33,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_424_425,plain,
! [X33,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_425_426,plain,
! [X61,X46,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X61)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X61)) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_426_427,plain,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X46)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46)) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_427_428,plain,
! [X58,X39,X26,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X39),X58)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X39),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X58)) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_428_429,plain,
! [X39,X26,X10,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X26),X39))
| ~ hBOOL(hAPP(hAPP(X10,X26),X39)) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_429_430,plain,
! [X48,X43,X56,X3] :
( c_List_Olistsp(X56,X43,X3)
| ~ c_List_Olistsp(X56,c_List_Oappend(X43,X48,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_430_431,plain,
! [X48,X43,X56,X3] :
( c_List_Olistsp(X56,X48,X3)
| ~ c_List_Olistsp(X56,c_List_Oappend(X43,X48,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_431_432,plain,
! [X10,X24,X20] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X10,c_Lambda_OdB_OVar(X20),X24)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_432_433,axiom,
! [X48,X39,X43,X3] :
( c_List_Orev(X43,X3) != c_List_Olist_OCons(X39,X48,X3)
| X43 = c_List_Oappend(c_List_Orev(X48,X3),c_List_Olist_OCons(X39,c_List_Olist_ONil(X3),X3),X3) ),
c_0_157 ).
fof(c_0_433_434,plain,
! [X39,X10,X33,X3] :
( c_Wellfounded_Oaccp(X10,X39,X3)
| ~ hBOOL(hAPP(hAPP(X10,X39),X33))
| ~ c_Wellfounded_Oaccp(X10,X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_434_435,plain,
! [X10,X47,X33,X3] :
( c_Wellfounded_Oaccp(X10,X33,X3)
| ~ hBOOL(hAPP(hAPP(X10,X33),X47))
| ~ c_Wellfounded_Oaccp(X10,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_435_436,plain,
! [X33,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_436_437,plain,
! [X33,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_437_438,plain,
! [X33,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X33,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_438_439,plain,
! [X10] :
( hBOOL(hAPP(c_InductTermi_OIT,X10))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X10,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_439_440,plain,
! [X26,X17,X31,X3] :
( c_List_Ofilter(X31,c_List_Oreplicate(X17,X26,X3),X3) = c_List_Oreplicate(X17,X26,X3)
| ~ hBOOL(hAPP(X31,X26)) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_440_441,plain,
! [X52,X15,X21,X23] :
( c_Type_Otyping(X21,X52,X23)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X15),X52))
| ~ c_Type_Otyping(X21,X15,X23) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_441_442,axiom,
! [X43,X26,X31,X3] :
( c_List_Oremove1(X26,c_List_Ofilter(X31,X43,X3),X3) = c_List_Ofilter(X31,X43,X3)
| hBOOL(hAPP(X31,X26)) ),
c_0_166 ).
fof(c_0_442_443,axiom,
! [X43,X26,X31,X3] :
( c_List_Ofilter(X31,c_List_Olist_OCons(X26,X43,X3),X3) = c_List_Ofilter(X31,X43,X3)
| hBOOL(hAPP(X31,X26)) ),
c_0_167 ).
fof(c_0_443_444,plain,
! [X58,X39,X26,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X58,X26,X3)
| ~ c_HOL_Oord__class_Oless(X58,X39,X3)
| ~ c_HOL_Oord__class_Oless(X39,X26,X3) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_444_445,plain,
! [X58,X39,X26,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X26,X58,X3)
| ~ c_HOL_Oord__class_Oless(X39,X58,X3)
| ~ c_HOL_Oord__class_Oless(X26,X39,X3) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_445_446,plain,
! [X15,X7] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X7)),c_Lambda_OdB_OAbs(X15)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X15)) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_446_447,plain,
! [X43,X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(X43,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X26,X43,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_447_448,plain,
! [X48,X43,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(X43,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X43,X48,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_448_449,plain,
! [X48,X43,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(X48,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X43,X48,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_449_450,axiom,
! [X48,X43,X26,X31,X3] :
( c_List_Olist_OCons(X26,X43,X3) != c_List_Ofilter(X31,X48,X3)
| hBOOL(hAPP(X31,X26)) ),
c_0_174 ).
fof(c_0_450_451,axiom,
! [X48,X43,X26,X31,X3] :
( c_List_Ofilter(X31,X48,X3) != c_List_Olist_OCons(X26,X43,X3)
| hBOOL(hAPP(X31,X26)) ),
c_0_175 ).
fof(c_0_451_452,axiom,
! [X26,X17,X31,X3] :
( c_List_Ofilter(X31,c_List_Oreplicate(X17,X26,X3),X3) = c_List_Olist_ONil(X3)
| hBOOL(hAPP(X31,X26)) ),
c_0_176 ).
fof(c_0_452_453,plain,
! [X15] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X15,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_453_454,axiom,
! [X17,X8,X31] :
( hBOOL(hAPP(hAPP(X31,X17),X8))
| c_HOL_Oord__class_Oless(X17,X8,tc_nat)
| X8 = X17
| c_HOL_Oord__class_Oless(X8,X17,tc_nat) ),
c_0_178 ).
fof(c_0_454_455,plain,
! [X58,X39,X26,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X39) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X58)
| X39 = X58 ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_455_456,plain,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X33)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X33)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_456_457,plain,
! [X47,X33,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X33,X47,X3)
| ~ c_HOL_Oord__class_Oless(X47,X33,X3) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_457_458,plain,
! [X39,X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X26,X39,X3)
| ~ c_HOL_Oord__class_Oless(X39,X26,X3) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_458_459,plain,
! [X39,X26,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X39,X26,X3)
| ~ c_HOL_Oord__class_Oless(X26,X39,X3) ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_459_460,plain,
! [X47,X33,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X47,X33,X3)
| ~ c_HOL_Oord__class_Oless(X33,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_460_461,axiom,
! [X43,X26,X3] :
( c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3) != c_List_Orev(X43,X3)
| X43 = c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3) ),
c_0_185 ).
fof(c_0_461_462,axiom,
! [X43,X26,X3] :
( c_List_Orev(X43,X3) != c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3)
| X43 = c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3) ),
c_0_186 ).
fof(c_0_462_463,axiom,
! [X39,X26,X17,X8,X3] :
( c_List_Oreplicate(X8,X26,X3) != c_List_Oreplicate(X17,X39,X3)
| X26 = X39
| X8 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_187 ).
fof(c_0_463_464,axiom,
! [X39,X26,X17,X8,X3] :
( c_List_Oreplicate(X8,X26,X3) != c_List_Oreplicate(X17,X39,X3)
| X8 = X17 ),
c_0_188 ).
fof(c_0_464_465,plain,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46)
| X47 = X46 ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_465_466,plain,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46)
| X47 = X46 ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_466_467,plain,
! [X46,X47,X33,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X33) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X33)
| X47 = X46 ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_467_468,axiom,
! [X36,X48,X43,X3] :
( c_List_Oappend(X48,X43,X3) != c_List_Oappend(X36,X43,X3)
| X48 = X36 ),
c_0_192 ).
fof(c_0_468_469,axiom,
! [X36,X48,X43,X3] :
( c_List_Oappend(X43,X48,X3) != c_List_Oappend(X43,X36,X3)
| X48 = X36 ),
c_0_193 ).
fof(c_0_469_470,axiom,
! [X53,X45,X54,X33,X3] :
( c_List_Olist_OCons(X33,X45,X3) != c_List_Olist_OCons(X54,X53,X3)
| X33 = X54 ),
c_0_194 ).
fof(c_0_470_471,axiom,
! [X53,X45,X54,X33,X3] :
( c_List_Olist_OCons(X33,X45,X3) != c_List_Olist_OCons(X54,X53,X3)
| X45 = X53 ),
c_0_195 ).
fof(c_0_471_472,axiom,
! [X26,X7] :
( c_HOL_Oord__class_Oless(X26,X26,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X26),X7,X26) = c_Lambda_Oliftn(X26,X7,c_HOL_Ozero__class_Ozero(tc_nat)) ),
c_0_196 ).
fof(c_0_472_473,plain,
! [X1,X2,X3] :
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_473_474,plain,
! [X33] :
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X33)))
| X33 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X33))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X33),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X33)) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_474_475,plain,
! [X43,X33,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(c_List_Oremove1(X33,X43,X3),X3)
| ~ c_List_Olinorder__class_Osorted(X43,X3) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_475_476,plain,
! [X40,X24,X20] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X24),X40,X20) = c_Lambda_OdB_OVar(X24)
| ~ c_HOL_Oord__class_Oless(X24,X20,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_476_477,plain,
! [X17,X44,X20] :
( c_Lambda_Oliftn(X17,c_Lambda_OdB_OVar(X20),X44) = c_Lambda_OdB_OVar(X20)
| ~ c_HOL_Oord__class_Oless(X20,X44,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_477_478,plain,
! [X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X26,c_List_Olist_ONil(X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_478_479,plain,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| hBOOL(hAPP(X31,v_sko__List__XdropWhile__Xinduct__2(X31)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_479_480,plain,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| hBOOL(hAPP(X31,v_sko__List__Xtake__Xinduct__2(X31)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_480_481,plain,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| hBOOL(hAPP(X31,v_sko__List__Xconcat__Xinduct__2(X31)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_481_482,plain,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| hBOOL(hAPP(X31,v_sko__List__Xdistinct__Xinduct__2(X31)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_482_483,plain,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| hBOOL(hAPP(X31,v_sko__List__Xremove1__Xinduct__2(X31)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_483_484,plain,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| hBOOL(hAPP(X31,v_sko__List__Xlist__Xinduct__2(X31)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_484_485,plain,
! [X45,X31] :
( hBOOL(hAPP(X31,X45))
| hBOOL(hAPP(X31,v_sko__List__Xmap__Xinduct__2(X31)))
| ~ hBOOL(hAPP(X31,c_List_Olist_ONil(t_a))) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_485_486,plain,
! [X37,X38,X33,X3] :
( hAPP(hAPP(X38,X33),X37) = X33
| ~ c_OrderedGroup_Omonoid__add(X37,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_486_487,plain,
! [X37,X38,X33,X3] :
( hAPP(hAPP(X38,X37),X33) = X33
| ~ c_OrderedGroup_Omonoid__add(X37,X38,X3) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_487_488,plain,
! [X15,X20] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X15,X20)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_488_489,axiom,
! [X7,X44,X20] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X20),X7,X44) = c_Lambda_OdB_OVar(X20)
| X20 = X44
| c_HOL_Oord__class_Oless(X44,X20,tc_nat) ),
c_0_213 ).
fof(c_0_489_490,axiom,
! [X7,X44,X20] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X20),X7,X44) = c_Lambda_OdB_OVar(X20)
| X20 = X44
| c_HOL_Oord__class_Oless(X44,X20,tc_nat) ),
c_0_214 ).
fof(c_0_490_491,axiom,
! [X43,X3] :
( c_Nat_Osize__class_Osize(c_List_Oremdups(X43,X3),tc_List_Olist(X3)) != c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3))
| c_List_Oremdups(X43,X3) = X43 ),
c_0_215 ).
fof(c_0_491_492,plain,
! [X39,X26,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X39,X26,X3)
| c_HOL_Oord__class_Oless(X26,X39,X3)
| X26 = X39 ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_492_493,plain,
! [X39,X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| X26 = X39
| c_HOL_Oord__class_Oless(X39,X26,X3)
| c_HOL_Oord__class_Oless(X26,X39,X3) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_493_494,plain,
! [X39,X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X39,X26,X3)
| c_HOL_Oord__class_Oless(X26,X39,X3)
| X26 = X39 ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_494_495,plain,
! [X39,X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X39,X26,X3)
| X26 = X39
| c_HOL_Oord__class_Oless(X26,X39,X3) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_495_496,plain,
! [X39,X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| X26 = X39
| c_HOL_Oord__class_Oless(X26,X39,X3)
| c_HOL_Oord__class_Oless(X39,X26,X3) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_496_497,axiom,
! [X65,X66,X67,X68] :
( hAPP(hAPP(c_Type_Otype_OFun,X68),X66) != hAPP(hAPP(c_Type_Otype_OFun,X67),X65)
| X66 = X65 ),
c_0_221 ).
fof(c_0_497_498,axiom,
! [X65,X66,X67,X68] :
( hAPP(hAPP(c_Type_Otype_OFun,X68),X66) != hAPP(hAPP(c_Type_Otype_OFun,X67),X65)
| X68 = X67 ),
c_0_222 ).
fof(c_0_498_499,axiom,
! [X11,X12,X13,X14] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X14),X12) != hAPP(hAPP(c_Lambda_OdB_OApp,X13),X11)
| X14 = X13 ),
c_0_223 ).
fof(c_0_499_500,axiom,
! [X11,X12,X13,X14] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X14),X12) != hAPP(hAPP(c_Lambda_OdB_OApp,X13),X11)
| X12 = X11 ),
c_0_224 ).
fof(c_0_500_501,axiom,
! [X26,X7] :
( c_HOL_Oord__class_Oless(X26,X26,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X26),X7,X26) = X7 ),
c_0_225 ).
fof(c_0_501_502,plain,
! [X46,X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X46),X33) ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_502_503,plain,
! [X47,X33,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X47) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X47),X33) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_503_504,plain,
! [X39,X26,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X39) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X39),X26) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_504_505,plain,
! [X20,X21,X23] :
( hAPP(X21,X20) = X23
| ~ c_Type_Otyping(X21,c_Lambda_OdB_OVar(X20),X23) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_505_506,axiom,
! [X17,X8] :
( c_HOL_Oord__class_Oless(X17,X8,tc_nat)
| c_HOL_Oord__class_Oless(X8,X17,tc_nat)
| X8 = X17 ),
c_0_230 ).
fof(c_0_506_507,axiom,
! [X39,X26] :
( c_HOL_Oord__class_Oless(X39,X26,tc_nat)
| c_HOL_Oord__class_Oless(X26,X39,tc_nat)
| X26 = X39 ),
c_0_231 ).
fof(c_0_507_508,plain,
! [X44,X20] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X20),X44) = c_Lambda_OdB_OVar(X20)
| ~ c_HOL_Oord__class_Oless(X20,X44,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_508_509,plain,
! [X26,X33,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X26 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),X33)
| X33 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_509_510,plain,
! [X33,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),X33) != c_HOL_Ozero__class_Ozero(X3)
| X33 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_510_511,axiom,
! [X43,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3)),tc_nat)
| X43 = c_List_Olist_ONil(X3) ),
c_0_235 ).
fof(c_0_511_512,axiom,
! [X43,X17,X3] :
( c_List_Orotate(X17,X43,X3) != c_List_Olist_ONil(X3)
| X43 = c_List_Olist_ONil(X3) ),
c_0_236 ).
fof(c_0_512_513,axiom,
! [X48,X43,X3] :
( c_List_Oappend(X43,X48,X3) != c_List_Olist_ONil(X3)
| X48 = c_List_Olist_ONil(X3) ),
c_0_237 ).
fof(c_0_513_514,axiom,
! [X48,X43,X3] :
( c_List_Oappend(X43,X48,X3) != c_List_Olist_ONil(X3)
| X43 = c_List_Olist_ONil(X3) ),
c_0_238 ).
fof(c_0_514_515,axiom,
! [X48,X43,X3] :
( c_List_Olist_ONil(X3) != c_List_Oappend(X43,X48,X3)
| X48 = c_List_Olist_ONil(X3) ),
c_0_239 ).
fof(c_0_515_516,axiom,
! [X48,X43,X3] :
( c_List_Olist_ONil(X3) != c_List_Oappend(X43,X48,X3)
| X43 = c_List_Olist_ONil(X3) ),
c_0_240 ).
fof(c_0_516_517,axiom,
! [X26,X17,X3] :
( c_List_Oreplicate(X17,X26,X3) != c_List_Olist_ONil(X3)
| X17 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_241 ).
fof(c_0_517_518,axiom,
! [X26,X17,X3] :
( c_List_Olist_ONil(X3) != c_List_Oreplicate(X17,X26,X3)
| X17 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_242 ).
fof(c_0_518_519,plain,
! [X26,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X26,X26,X3) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_519_520,plain,
! [X26,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X26,X26,X3) ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_520_521,plain,
! [X26,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X26,X26,X3) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_521_522,axiom,
! [X48,X43,X3] :
( X48 != c_List_Oappend(X43,X48,X3)
| X43 = c_List_Olist_ONil(X3) ),
c_0_246 ).
fof(c_0_522_523,axiom,
! [X48,X43,X3] :
( c_List_Oappend(X43,X48,X3) != X48
| X43 = c_List_Olist_ONil(X3) ),
c_0_247 ).
fof(c_0_523_524,axiom,
! [X48,X43,X3] :
( X43 != c_List_Oappend(X43,X48,X3)
| X48 = c_List_Olist_ONil(X3) ),
c_0_248 ).
fof(c_0_524_525,axiom,
! [X48,X43,X3] :
( c_List_Oappend(X43,X48,X3) != X43
| X48 = c_List_Olist_ONil(X3) ),
c_0_249 ).
fof(c_0_525_526,axiom,
! [X43,X3] :
( c_List_Oremdups(X43,X3) != X43
| c_Nat_Osize__class_Osize(c_List_Oremdups(X43,X3),tc_List_Olist(X3)) = c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3)) ),
c_0_250 ).
fof(c_0_526_527,plain,
! [X10] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X10)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_527_528,plain,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_528_529,plain,
! [X26,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X26 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X26),c_HOL_Ozero__class_Ozero(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_529_530,plain,
! [X26,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X26) = X26 ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_530_531,plain,
! [X33,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X33) = X33 ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_531_532,plain,
! [X33,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X33) = X33 ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_532_533,plain,
! [X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X33) = X33 ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_533_534,plain,
! [X49,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(c_List_Oremdups(X49,X3),X3)
| ~ c_List_Olinorder__class_Osorted(X49,X3) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_534_535,plain,
! [X33,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Ozero__class_Ozero(X3)) = X33 ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_535_536,plain,
! [X33,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Ozero__class_Ozero(X3)) = X33 ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_536_537,plain,
! [X33,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X33),c_HOL_Ozero__class_Ozero(X3)) = X33 ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_537_538,axiom,
! [X17] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X17,tc_nat)
| X17 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_262 ).
fof(c_0_538_539,axiom,
! [X48,X43,X3] :
( c_List_Orev(X43,X3) != c_List_Orev(X48,X3)
| X43 = X48 ),
c_0_263 ).
fof(c_0_539_540,axiom,
! [X43,X3] :
( c_Nat_Osize__class_Osize(X43,tc_List_Olist(X3)) != c_HOL_Ozero__class_Ozero(tc_nat)
| X43 = c_List_Olist_ONil(X3) ),
c_0_264 ).
fof(c_0_540_541,plain,
! [X4,X5] :
( class_Orderings_Opreorder(tc_fun(X4,X5))
| ~ class_Orderings_Opreorder(X5) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_541_542,plain,
! [X4,X5] :
( class_Orderings_Oorder(tc_fun(X4,X5))
| ~ class_Orderings_Oorder(X5) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_542_543,axiom,
! [X26,X3] :
( c_List_Oremdups(X26,X3) != c_List_Olist_ONil(X3)
| X26 = c_List_Olist_ONil(X3) ),
c_0_267 ).
fof(c_0_543_544,axiom,
! [X43,X3] :
( c_List_Olist_ONil(X3) != c_List_Orev(X43,X3)
| X43 = c_List_Olist_ONil(X3) ),
c_0_268 ).
fof(c_0_544_545,axiom,
! [X26,X3] :
( c_List_Olist_ONil(X3) != c_List_Oremdups(X26,X3)
| X26 = c_List_Olist_ONil(X3) ),
c_0_269 ).
fof(c_0_545_546,axiom,
! [X43,X3] :
( c_List_Orev(X43,X3) != c_List_Olist_ONil(X3)
| X43 = c_List_Olist_ONil(X3) ),
c_0_270 ).
fof(c_0_546_547,plain,
! [X3] :
( ~ class_OrderedGroup_Osemigroup__add(X3)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_547_548,plain,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| c_List_Olinorder__class_Osorted(c_List_Olist_ONil(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_548_549,axiom,
! [X57,X55] :
( c_Lambda_OdB_OAbs(X55) != c_Lambda_OdB_OAbs(X57)
| X55 = X57 ),
c_0_273 ).
fof(c_0_549_550,axiom,
! [X18,X19] :
( c_Lambda_OdB_OVar(X19) != c_Lambda_OdB_OVar(X18)
| X19 = X18 ),
c_0_274 ).
fof(c_0_550_551,plain,
! [X36,X37,X38,X39,X40,X41,X42] :
( X40 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X42,X40,X39,X36),X42,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X39,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X38),X37,tc_Lambda_OdB,tc_Lambda_OdB),X40)
| ~ c_Type_Otypings(X39,X37,X41)
| ~ c_Type_Otyping(X39,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X38),X37,tc_Lambda_OdB,tc_Lambda_OdB),X36,tc_Lambda_OdB,tc_Lambda_OdB),X42) ),
inference(variable_rename,[status(thm)],[c_0_275]) ).
fof(c_0_551_552,plain,
! [X28,X29,X30] :
( X28 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X30),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X30,X29,X28),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X30),X29,tc_Lambda_OdB,tc_Lambda_OdB)),X28)) ),
inference(variable_rename,[status(thm)],[c_0_276]) ).
fof(c_0_552_553,plain,
! [X36,X37,X38,X39,X40,X41,X42] :
( c_Type_Otypings(X39,X36,c_Type_Osko__Type__Xvar__app__types__1__1(X42,X40,X39,X36))
| ~ c_Type_Otyping(X39,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X38),X37,tc_Lambda_OdB,tc_Lambda_OdB),X40)
| ~ c_Type_Otypings(X39,X37,X41)
| ~ c_Type_Otyping(X39,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X38),X37,tc_Lambda_OdB,tc_Lambda_OdB),X36,tc_Lambda_OdB,tc_Lambda_OdB),X42) ),
inference(variable_rename,[status(thm)],[c_0_277]) ).
fof(c_0_553_554,plain,
! [X28,X29,X30] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X29,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X30,X29,X28),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X30),X29,tc_Lambda_OdB,tc_Lambda_OdB)),X28)) ),
inference(variable_rename,[status(thm)],[c_0_278]) ).
fof(c_0_554_555,plain,
! [X32,X33] :
( ~ hBOOL(hAPP(X33,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X33)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X33),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X33,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X33)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X33),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(X33,X32)) ),
inference(variable_rename,[status(thm)],[c_0_279]) ).
fof(c_0_555_556,plain,
! [X32,X33] :
( hBOOL(hAPP(X33,X32))
| ~ hBOOL(hAPP(X33,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X33)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X33),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X33,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X33)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X33),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(variable_rename,[status(thm)],[c_0_280]) ).
fof(c_0_556_557,plain,
! [X17,X18,X19] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X18,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X17,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X18,X17,tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_281])])]) ).
fof(c_0_557_558,plain,
! [X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X13,X11,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X11,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X13),X12)) ),
inference(variable_rename,[status(thm)],[c_0_282]) ).
fof(c_0_558_559,plain,
! [X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X13,X11,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X11,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X13),X12)) ),
inference(variable_rename,[status(thm)],[c_0_283]) ).
fof(c_0_559_560,plain,
! [X11,X12,X13] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X13)),X12),X11,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X12))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X13,X12,c_HOL_Ozero__class_Ozero(tc_nat)),X11,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(variable_rename,[status(thm)],[c_0_284]) ).
fof(c_0_560_561,plain,
! [X46,X47,X48,X49,X50] :
( ~ hBOOL(hAPP(X50,c_List_Olist_Olist__case(X48,X47,c_List_Olist_OCons(X49,X46,t_b),t_a,t_b)))
| hBOOL(hAPP(X50,hAPP(hAPP(X47,X49),X46))) ),
inference(variable_rename,[status(thm)],[c_0_285]) ).
fof(c_0_561_562,plain,
! [X43,X44,X45,X46,X47] :
( ~ hBOOL(hAPP(X47,c_List_Olist_Olist__case(X46,X45,c_List_Olist_OCons(X44,X43,t_b),t_a,t_b)))
| hBOOL(hAPP(X47,hAPP(hAPP(X45,X44),X43))) ),
inference(variable_rename,[status(thm)],[c_0_286]) ).
fof(c_0_562_563,plain,
! [X43,X44,X45,X46,X47,X48] :
( ~ hBOOL(hAPP(X48,c_Lambda_OdB_OdB__case(X47,X46,X45,hAPP(hAPP(c_Lambda_OdB_OApp,X44),X43),t_a)))
| hBOOL(hAPP(X48,hAPP(hAPP(X46,X44),X43))) ),
inference(variable_rename,[status(thm)],[c_0_287]) ).
fof(c_0_563_564,plain,
! [X32,X33,X34,X35,X36,X37] :
( ~ hBOOL(hAPP(X37,c_Lambda_OdB_OdB__case(X34,X33,X32,hAPP(hAPP(c_Lambda_OdB_OApp,X36),X35),t_a)))
| hBOOL(hAPP(X37,hAPP(hAPP(X33,X36),X35))) ),
inference(variable_rename,[status(thm)],[c_0_288]) ).
fof(c_0_564_565,plain,
! [X32,X33] :
( hBOOL(hAPP(X33,c_ListApplication_Osko__ListApplication__Xlem__1__3(X33)))
| ~ hBOOL(hAPP(X33,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X33)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X33),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(X33,X32)) ),
inference(variable_rename,[status(thm)],[c_0_289]) ).
fof(c_0_565_566,plain,
! [X32,X33] :
( hBOOL(hAPP(X33,X32))
| hBOOL(hAPP(X33,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X33)))
| ~ hBOOL(hAPP(X33,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X33)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X33),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(variable_rename,[status(thm)],[c_0_290]) ).
fof(c_0_566_567,plain,
! [X24,X25,X26,X27,X28] :
( X28 = X27
| ~ c_Type_Otyping(X26,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X25),X24,tc_Lambda_OdB,tc_Lambda_OdB),X27)
| ~ c_Type_Otyping(X26,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X25),X24,tc_Lambda_OdB,tc_Lambda_OdB),X28) ),
inference(variable_rename,[status(thm)],[c_0_291]) ).
fof(c_0_567_568,plain,
! [X56,X57,X58,X59,X60] :
( ~ hBOOL(hAPP(X60,c_Lambda_OdB_OdB__case(X58,X57,X56,c_Lambda_OdB_OAbs(X59),t_a)))
| hBOOL(hAPP(X60,hAPP(X56,X59))) ),
inference(variable_rename,[status(thm)],[c_0_292]) ).
fof(c_0_568_569,plain,
! [X32,X33,X34,X35,X36] :
( ~ hBOOL(hAPP(X36,c_Lambda_OdB_OdB__case(X35,X34,X33,c_Lambda_OdB_OAbs(X32),t_a)))
| hBOOL(hAPP(X36,hAPP(X33,X32))) ),
inference(variable_rename,[status(thm)],[c_0_293]) ).
fof(c_0_569_570,plain,
! [X33,X34,X35,X36,X37] :
( ~ hBOOL(hAPP(X37,c_Lambda_OdB_OdB__case(X36,X35,X34,c_Lambda_OdB_OVar(X33),t_a)))
| hBOOL(hAPP(X37,hAPP(X36,X33))) ),
inference(variable_rename,[status(thm)],[c_0_294]) ).
fof(c_0_570_571,plain,
! [X32,X33,X34,X35,X36] :
( ~ hBOOL(hAPP(X36,c_Lambda_OdB_OdB__case(X35,X34,X33,c_Lambda_OdB_OVar(X32),t_a)))
| hBOOL(hAPP(X36,hAPP(X35,X32))) ),
inference(variable_rename,[status(thm)],[c_0_295]) ).
fof(c_0_571_572,plain,
! [X32,X33,X34] :
( ~ hBOOL(hAPP(X34,c_List_Olist_Olist__case(X33,X32,c_List_Olist_ONil(t_b),t_a,t_b)))
| hBOOL(hAPP(X34,X33)) ),
inference(variable_rename,[status(thm)],[c_0_296]) ).
fof(c_0_572_573,plain,
! [X11,X12,X13] :
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X13,X12,c_HOL_Ozero__class_Ozero(tc_nat)),X11,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X12,tc_Lambda_OdB)
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X13)),X12),X11,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_297]) ).
fof(c_0_573_574,plain,
! [X24,X25,X26,X27] :
( c_Type_Otyping(X26,c_Lambda_OdB_OVar(X25),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X27,X26,X25,X24),X27,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X26,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X25),X24,tc_Lambda_OdB,tc_Lambda_OdB),X27) ),
inference(variable_rename,[status(thm)],[c_0_298]) ).
fof(c_0_574_575,plain,
! [X24,X25,X26,X27] :
( c_Type_Otyping(X26,X25,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X27,X26,X25,X24),X27,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X26,c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X24,tc_Lambda_OdB,tc_Lambda_OdB),X27) ),
inference(variable_rename,[status(thm)],[c_0_299]) ).
fof(c_0_575_576,plain,
! [X24,X25,X26,X27] :
( c_Type_Otyping(X26,X25,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X27,X26,X25,X24),X27,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X26,c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X24,tc_Lambda_OdB,tc_Lambda_OdB),X27) ),
inference(variable_rename,[status(thm)],[c_0_300]) ).
fof(c_0_576_577,plain,
! [X34] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X34),v_sko__InductTermi__XIT__Xcases__5(X34),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X34),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X34)))
| X34 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X34)),v_sko__InductTermi__XIT__Xcases__1(X34),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
inference(variable_rename,[status(thm)],[c_0_301]) ).
fof(c_0_577_578,plain,
! [X34] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X34),v_sko__InductTermi__XIT__Xcases__5(X34),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X34),tc_Lambda_OdB,tc_Lambda_OdB)))
| X34 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X34))
| X34 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X34)),v_sko__InductTermi__XIT__Xcases__1(X34),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
inference(variable_rename,[status(thm)],[c_0_302]) ).
fof(c_0_578_579,plain,
! [X27,X28,X29] :
( c_List_Oappend(X27,c_List_Olist_OCons(X29,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X29) = c_List_Ofoldl(c_Lambda_OdB_OApp,X28,c_List_Oappend(X27,c_List_Olist_OCons(X29,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_303]) ).
fof(c_0_579_580,plain,
! [X36,X37,X38,X39,X40] :
( c_Type_Otyping(X38,c_List_Ofoldl(c_Lambda_OdB_OApp,X37,X36,tc_Lambda_OdB,tc_Lambda_OdB),X40)
| ~ c_Type_Otypings(X38,X36,X39)
| ~ c_Type_Otyping(X38,X37,c_List_Ofoldr(c_Type_Otype_OFun,X39,X40,tc_Type_Otype,tc_Type_Otype)) ),
inference(variable_rename,[status(thm)],[c_0_304]) ).
fof(c_0_580_581,plain,
! [X34] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X34),v_sko__InductTermi__XIT__Xcases__5(X34),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X34),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X34)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X34),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
inference(variable_rename,[status(thm)],[c_0_305]) ).
fof(c_0_581_582,plain,
! [X34] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X34),v_sko__InductTermi__XIT__Xcases__5(X34),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X34),tc_Lambda_OdB,tc_Lambda_OdB)))
| X34 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X34))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X34),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
inference(variable_rename,[status(thm)],[c_0_306]) ).
fof(c_0_582_583,plain,
! [X18,X19] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X19),X18,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X18,tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_307])])]) ).
fof(c_0_583_584,plain,
! [X24,X25,X26,X27] :
( c_Type_Otypings(X26,X24,c_Type_Osko__Type__Xvar__app__typesE__1__1(X27,X26,X25,X24))
| ~ c_Type_Otyping(X26,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X25),X24,tc_Lambda_OdB,tc_Lambda_OdB),X27) ),
inference(variable_rename,[status(thm)],[c_0_308]) ).
fof(c_0_584_585,plain,
! [X24,X25,X26,X27] :
( c_Type_Otypings(X26,X24,c_Type_Osko__Type__Xlist__app__typeD__1__1(X27,X26,X25,X24))
| ~ c_Type_Otyping(X26,c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X24,tc_Lambda_OdB,tc_Lambda_OdB),X27) ),
inference(variable_rename,[status(thm)],[c_0_309]) ).
fof(c_0_585_586,plain,
! [X24,X25,X26,X27] :
( c_Type_Otypings(X26,X24,c_Type_Osko__Type__Xlist__app__typeE__1__1(X27,X26,X25,X24))
| ~ c_Type_Otyping(X26,c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X24,tc_Lambda_OdB,tc_Lambda_OdB),X27) ),
inference(variable_rename,[status(thm)],[c_0_310]) ).
fof(c_0_586_587,plain,
! [X17,X18,X19,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X18),X17,tc_Lambda_OdB,tc_Lambda_OdB)
| X20 = X18 ),
inference(variable_rename,[status(thm)],[c_0_311]) ).
fof(c_0_587_588,plain,
! [X17,X18,X19,X20] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X20),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X18),X17,tc_Lambda_OdB,tc_Lambda_OdB)
| X19 = X17 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_312])])]) ).
fof(c_0_588_589,plain,
! [X18,X19,X20,X21] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X21),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X18,tc_Lambda_OdB,tc_Lambda_OdB)
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_313]) ).
fof(c_0_589_590,plain,
! [X18,X19,X20,X21] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X21),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X18,tc_Lambda_OdB,tc_Lambda_OdB)
| X19 = X18 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_314])])]) ).
fof(c_0_590_591,plain,
! [X40,X41,X42,X43] :
( ~ class_OrderedGroup_Osemigroup__add(X43)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X43),X42),X41),X40,X43,X43) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X43),X42),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X43),X41,X40,X43,X43)) ),
inference(variable_rename,[status(thm)],[c_0_315]) ).
fof(c_0_591_592,plain,
! [X11,X12,X13] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X13,X11,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X11,tc_Lambda_OdB,tc_Lambda_OdB)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_316]) ).
fof(c_0_592_593,plain,
! [X40,X41,X42,X43,X44] :
( c_List_Ofoldl(X43,hAPP(hAPP(X43,X42),X41),X40,X44,X44) = hAPP(hAPP(X43,X42),c_List_Ofoldl(X43,X41,X40,X44,X44))
| ~ c_OrderedGroup_Osemigroup__add(X43,X44) ),
inference(variable_rename,[status(thm)],[c_0_317]) ).
fof(c_0_593_594,plain,
! [X39,X40,X41,X42,X43] :
( hAPP(hAPP(X42,X41),c_List_Ofoldl(X42,X40,X39,X43,X43)) = c_List_Ofoldl(X42,X41,X39,X43,X43)
| ~ c_OrderedGroup_Omonoid__add(X40,X42,X43) ),
inference(variable_rename,[status(thm)],[c_0_318]) ).
fof(c_0_594_595,plain,
! [X44,X45,X46] :
( ~ class_OrderedGroup_Omonoid__add(X46)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X46),X45,X44,X46,X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X46),X45),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X46),X44,c_HOL_Ozero__class_Ozero(X46),X46,X46)) ),
inference(variable_rename,[status(thm)],[c_0_319]) ).
fof(c_0_595_596,plain,
! [X37,X38,X39] :
( ~ class_OrderedGroup_Omonoid__add(X39)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X39),X38),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X39),c_HOL_Ozero__class_Ozero(X39),X37,X39,X39)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X39),X38,X37,X39,X39) ),
inference(variable_rename,[status(thm)],[c_0_320]) ).
fof(c_0_596_597,plain,
! [X16,X17,X18,X19] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X19),X18) != c_List_Ofoldl(c_Lambda_OdB_OApp,X17,X16,tc_Lambda_OdB,tc_Lambda_OdB)
| X19 = c_List_Ofoldl(c_Lambda_OdB_OApp,X17,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X19,X18,X17,X16),tc_Lambda_OdB,tc_Lambda_OdB)
| X16 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_321]) ).
fof(c_0_597_598,plain,
! [X26,X27,X28] :
( X28 != c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X27),X26,tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X28),X27) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X27),c_List_Oappend(X26,c_List_Olist_OCons(X27,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_322]) ).
fof(c_0_598_599,plain,
! [X34] :
( X34 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X34))),v_sko__InductTermi__XIT__Xcases__5(X34)),v_sko__InductTermi__XIT__Xcases__6(X34),tc_Lambda_OdB,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X34)))
| X34 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X34)),v_sko__InductTermi__XIT__Xcases__1(X34),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
inference(variable_rename,[status(thm)],[c_0_323]) ).
fof(c_0_599_600,plain,
! [X34] :
( X34 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X34))),v_sko__InductTermi__XIT__Xcases__5(X34)),v_sko__InductTermi__XIT__Xcases__6(X34),tc_Lambda_OdB,tc_Lambda_OdB)
| X34 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X34))
| X34 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X34)),v_sko__InductTermi__XIT__Xcases__1(X34),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
inference(variable_rename,[status(thm)],[c_0_324]) ).
fof(c_0_600_601,plain,
! [X16,X17,X18,X19] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X19),X18) != c_List_Ofoldl(c_Lambda_OdB_OApp,X17,X16,tc_Lambda_OdB,tc_Lambda_OdB)
| X16 = c_List_Oappend(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X19,X18,X17,X16),c_List_Olist_OCons(X18,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)
| X16 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_325]) ).
fof(c_0_601_602,plain,
! [X64,X65,X66,X67,X68,X69] :
( c_Nat_Osize__class_Osize(X66,tc_List_Olist(X69)) != c_Nat_Osize__class_Osize(X65,tc_List_Olist(X68))
| c_Map_Omap__upds(X67,c_List_Oappend(X66,X64,X69),X65,X69,X68) = c_Map_Omap__upds(X67,X66,X65,X69,X68) ),
inference(variable_rename,[status(thm)],[c_0_326]) ).
fof(c_0_602_603,plain,
! [X64,X65,X66,X67,X68,X69] :
( c_Nat_Osize__class_Osize(X66,tc_List_Olist(X69)) != c_Nat_Osize__class_Osize(X65,tc_List_Olist(X68))
| c_Map_Omap__upds(X67,X66,c_List_Oappend(X65,X64,X68),X69,X68) = c_Map_Omap__upds(X67,X66,X65,X69,X68) ),
inference(variable_rename,[status(thm)],[c_0_327]) ).
fof(c_0_603_604,plain,
! [X44,X45] :
( ~ class_OrderedGroup_Omonoid__add(X45)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X45),c_HOL_Ozero__class_Ozero(X45),X44,X45,X45) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X45),X44,c_HOL_Ozero__class_Ozero(X45),X45,X45) ),
inference(variable_rename,[status(thm)],[c_0_328]) ).
fof(c_0_604_605,plain,
! [X44,X45,X46] :
( ~ class_OrderedGroup_Oab__semigroup__add(X46)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X46),X44,X45,X46,X46) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X46),X45,X44,X46,X46) ),
inference(variable_rename,[status(thm)],[c_0_329]) ).
fof(c_0_605_606,plain,
! [X16,X17,X18] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X18),X17) != c_List_Ofoldl(c_Lambda_OdB_OApp,X16,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X18),X17) = X16 ),
inference(variable_rename,[status(thm)],[c_0_330]) ).
fof(c_0_606_607,plain,
! [X11,X12,X13] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X11,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X13)
| X12 = c_Lambda_OdB_OAbs(X13) ),
inference(variable_rename,[status(thm)],[c_0_331]) ).
fof(c_0_607_608,plain,
! [X11,X12,X13] :
( c_Lambda_OdB_OAbs(X13) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X11,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X13) = X12 ),
inference(variable_rename,[status(thm)],[c_0_332]) ).
fof(c_0_608_609,plain,
! [X9,X10,X11] :
( c_Lambda_OdB_OVar(X11) != c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X9,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X11) = X10 ),
inference(variable_rename,[status(thm)],[c_0_333]) ).
fof(c_0_609_610,plain,
! [X11,X12,X13] :
( c_Lambda_OdB_OAbs(X13) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X11,tc_Lambda_OdB,tc_Lambda_OdB)
| X11 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_334])])]) ).
fof(c_0_610_611,plain,
! [X11,X12,X13] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X11,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X13)
| X11 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_335])])]) ).
fof(c_0_611_612,plain,
! [X9,X10,X11] :
( c_Lambda_OdB_OVar(X11) != c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X9,tc_Lambda_OdB,tc_Lambda_OdB)
| X9 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_336])])]) ).
fof(c_0_612_613,plain,
! [X40,X41,X42,X43] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X42,X43),X40),X41))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X42,X43,X43),X43),X41),X40)) ),
inference(variable_rename,[status(thm)],[c_0_337]) ).
fof(c_0_613_614,plain,
! [X49,X50,X51,X52,X53,X54] :
( hBOOL(hAPP(hAPP(X53,X50),X52))
| c_ListOrder_Ostep1(X53,X49,X51,X54)
| ~ c_ListOrder_Ostep1(X53,c_List_Oappend(X49,c_List_Olist_OCons(X50,c_List_Olist_ONil(X54),X54),X54),c_List_Oappend(X51,c_List_Olist_OCons(X52,c_List_Olist_ONil(X54),X54),X54),X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_338])])]) ).
fof(c_0_614_615,plain,
! [X49,X50,X51,X52,X53,X54] :
( X49 = X51
| c_ListOrder_Ostep1(X53,X49,X51,X54)
| ~ c_ListOrder_Ostep1(X53,c_List_Oappend(X49,c_List_Olist_OCons(X50,c_List_Olist_ONil(X54),X54),X54),c_List_Oappend(X51,c_List_Olist_OCons(X52,c_List_Olist_ONil(X54),X54),X54),X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_339])])]) ).
fof(c_0_615_616,plain,
! [X49,X50,X51,X52,X53,X54] :
( hBOOL(hAPP(hAPP(X53,X50),X52))
| X50 = X52
| ~ c_ListOrder_Ostep1(X53,c_List_Oappend(X49,c_List_Olist_OCons(X50,c_List_Olist_ONil(X54),X54),X54),c_List_Oappend(X51,c_List_Olist_OCons(X52,c_List_Olist_ONil(X54),X54),X54),X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_340])])]) ).
fof(c_0_616_617,plain,
! [X34] :
( X34 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X34))),v_sko__InductTermi__XIT__Xcases__5(X34)),v_sko__InductTermi__XIT__Xcases__6(X34),tc_Lambda_OdB,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X34)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X34),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
inference(variable_rename,[status(thm)],[c_0_341]) ).
fof(c_0_617_618,plain,
! [X52,X53,X54,X55,X56,X57] :
( c_List_Olist__update(c_List_Olist__update(X52,X56,X54,X57),X55,X53,X57) = c_List_Olist__update(c_List_Olist__update(X52,X55,X53,X57),X56,X54,X57)
| X56 = X55 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_342])])]) ).
fof(c_0_618_619,plain,
! [X49,X50,X51,X52,X53,X54] :
( X49 = X51
| X50 = X52
| ~ c_ListOrder_Ostep1(X53,c_List_Oappend(X49,c_List_Olist_OCons(X50,c_List_Olist_ONil(X54),X54),X54),c_List_Oappend(X51,c_List_Olist_OCons(X52,c_List_Olist_ONil(X54),X54),X54),X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_343])])]) ).
fof(c_0_619_620,plain,
! [X34] :
( X34 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X34))),v_sko__InductTermi__XIT__Xcases__5(X34)),v_sko__InductTermi__XIT__Xcases__6(X34),tc_Lambda_OdB,tc_Lambda_OdB)
| X34 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X34))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X34),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
inference(variable_rename,[status(thm)],[c_0_344]) ).
fof(c_0_620_621,plain,
! [X34] :
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X34)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X34)))
| X34 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X34)),v_sko__InductTermi__XIT__Xcases__1(X34),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
inference(variable_rename,[status(thm)],[c_0_345]) ).
fof(c_0_621_622,plain,
! [X40,X41,X42,X43] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X42,X43,X43),X43),X41),X40))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X42,X43),X40),X41)) ),
inference(variable_rename,[status(thm)],[c_0_346]) ).
fof(c_0_622_623,plain,
! [X34] :
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X34)))
| X34 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X34))
| X34 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X34)),v_sko__InductTermi__XIT__Xcases__1(X34),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
inference(variable_rename,[status(thm)],[c_0_347]) ).
fof(c_0_623_624,plain,
! [X36,X37,X38,X39] :
( c_Type_Otypings(X38,X36,c_Type_Osko__Type__Xtypes__snocE__1__1(X39,X38,X37,X36))
| ~ c_Type_Otypings(X38,c_List_Oappend(X36,c_List_Olist_OCons(X37,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X39) ),
inference(variable_rename,[status(thm)],[c_0_348]) ).
fof(c_0_624_625,plain,
! [X36,X37,X38,X39] :
( c_Type_Otyping(X38,X37,c_Type_Osko__Type__Xtypes__snocE__1__2(X39,X38,X37,X36))
| ~ c_Type_Otypings(X38,c_List_Oappend(X36,c_List_Olist_OCons(X37,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X39) ),
inference(variable_rename,[status(thm)],[c_0_349]) ).
fof(c_0_625_626,plain,
! [X60,X61,X62,X63] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X63),X61)),hAPP(hAPP(c_Lambda_OdB_OApp,X62),X60)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X61),X60))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X63),X62)) ),
inference(variable_rename,[status(thm)],[c_0_350]) ).
fof(c_0_626_627,plain,
! [X21,X22,X23,X24] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X23,X21,X24)),c_Lambda_Osubst(X22,X21,X24)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X23),X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_351])])]) ).
fof(c_0_627_628,plain,
! [X21,X22,X23,X24] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X21,X23,X24)),c_Lambda_Osubst(X21,X22,X24)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X23),X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_352])])]) ).
fof(c_0_628_629,plain,
! [X49,X50,X51,X52,X53,X54] :
( c_ListOrder_Ostep1(X53,X49,X51,X54)
| hBOOL(hAPP(hAPP(X53,X50),X52))
| ~ c_ListOrder_Ostep1(X53,c_List_Olist_OCons(X50,X49,X54),c_List_Olist_OCons(X52,X51,X54),X54) ),
inference(variable_rename,[status(thm)],[c_0_353]) ).
fof(c_0_629_630,plain,
! [X49,X50,X51,X52,X53] :
( c_List_Olist__update(c_List_Oappend(X50,X49,X53),X52,X51,X53) = c_List_Oappend(c_List_Olist__update(X50,X52,X51,X53),X49,X53)
| ~ c_HOL_Oord__class_Oless(X52,c_Nat_Osize__class_Osize(X50,tc_List_Olist(X53)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_354]) ).
fof(c_0_630_631,plain,
! [X49,X50,X51,X52,X53] :
( c_List_Olist__update(c_List_Oappend(X50,X49,X53),X52,X51,X53) = c_List_Oappend(c_List_Olist__update(X50,X52,X51,X53),X49,X53)
| ~ c_HOL_Oord__class_Oless(X52,c_Nat_Osize__class_Osize(X50,tc_List_Olist(X53)),tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_355]) ).
fof(c_0_631_632,plain,
! [X49,X50,X51,X52,X53,X54] :
( c_List_Olistrelp(X53,c_List_Olist_OCons(X52,X51,X54),c_List_Olist_OCons(X50,X49,X54),X54)
| ~ c_List_Olistrelp(X53,X51,X49,X54)
| ~ hBOOL(hAPP(hAPP(X53,X52),X50)) ),
inference(variable_rename,[status(thm)],[c_0_356]) ).
fof(c_0_632_633,plain,
! [X49,X50,X51,X52,X53,X54] :
( c_ListOrder_Ostep1(X53,X49,X51,X54)
| X51 = X49
| ~ c_ListOrder_Ostep1(X53,c_List_Olist_OCons(X50,X49,X54),c_List_Olist_OCons(X52,X51,X54),X54) ),
inference(variable_rename,[status(thm)],[c_0_357]) ).
fof(c_0_633_634,plain,
! [X21,X22,X23,X24] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X21,X23,X24)),c_Lambda_Osubst(X21,X22,X24)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X23),X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_358])])]) ).
fof(c_0_634_635,plain,
! [X64,X65,X66,X67,X68] :
( hBOOL(hAPP(hAPP(X64,X65),X66))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X64,X68,X67),X66),X65)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_359])])]) ).
fof(c_0_635_636,plain,
! [X71,X72,X73,X74,X75] :
( hBOOL(hAPP(hAPP(X71,X72),X73))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X71,X75,X74),X73),X72)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_360])])]) ).
fof(c_0_636_637,plain,
! [X49,X50,X51,X52,X53] :
( ~ c_ListOrder_Ostep1(X52,X49,X50,X53)
| c_ListOrder_Ostep1(X52,c_List_Oappend(X49,X51,X53),c_List_Oappend(X50,X51,X53),X53) ),
inference(variable_rename,[status(thm)],[c_0_361]) ).
fof(c_0_637_638,plain,
! [X61,X62,X63,X64,X65] :
( c_ListOrder_Ostep1(X64,c_List_Oappend(X61,X62,X65),c_List_Oappend(X61,X63,X65),X65)
| ~ c_ListOrder_Ostep1(X64,X62,X63,X65) ),
inference(variable_rename,[status(thm)],[c_0_362]) ).
fof(c_0_638_639,plain,
! [X49,X50,X51,X52,X53] :
( c_ListOrder_Ostep1(X52,c_List_Olist_OCons(X51,X49,X53),c_List_Olist_OCons(X51,X50,X53),X53)
| ~ c_ListOrder_Ostep1(X52,X49,X50,X53) ),
inference(variable_rename,[status(thm)],[c_0_363]) ).
fof(c_0_639_640,plain,
! [X60,X61,X62] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X62),X60)),hAPP(hAPP(c_Lambda_OdB_OApp,X61),X60)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X62),X61)) ),
inference(variable_rename,[status(thm)],[c_0_364]) ).
fof(c_0_640_641,plain,
! [X53,X54,X55] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X55),X54)),hAPP(hAPP(c_Lambda_OdB_OApp,X55),X53)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X54),X53)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_365])])]) ).
fof(c_0_641_642,plain,
! [X21,X22,X23,X24] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X23,X21,X24)),c_Lambda_Osubst(X22,X21,X24)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X23),X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_366])])]) ).
fof(c_0_642_643,plain,
! [X43,X44,X45,X46,X47] :
( ~ hBOOL(hAPP(X46,X45))
| hBOOL(hAPP(X46,c_List_Osko__List__XCons__eq__filter__iff__1__3(X46,X44,X47)))
| c_List_Olist_OCons(X45,c_List_Ofilter(X46,X43,X47),X47) = c_List_Ofilter(X46,c_List_Oappend(X44,c_List_Olist_OCons(X45,X43,X47),X47),X47) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_367])])]) ).
fof(c_0_643_644,plain,
! [X43,X44,X45,X46,X47] :
( ~ hBOOL(hAPP(X46,X45))
| hBOOL(hAPP(X46,c_List_Osko__List__Xfilter__eq__Cons__iff__1__3(X46,X44,X47)))
| c_List_Ofilter(X46,c_List_Oappend(X44,c_List_Olist_OCons(X45,X43,X47),X47),X47) = c_List_Olist_OCons(X45,c_List_Ofilter(X46,X43,X47),X47) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_368])])]) ).
fof(c_0_644_645,plain,
! [X64,X65,X66,X67,X68] :
( c_List_Omap(X66,X65,X67,X68) != c_List_Omap(X66,X64,X67,X68)
| c_Nat_Osize__class_Osize(X65,tc_List_Olist(X67)) = c_Nat_Osize__class_Osize(X64,tc_List_Olist(X67)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_369])])]) ).
fof(c_0_645_646,plain,
! [X49,X50,X51,X52,X53,X54] :
( X52 = X50
| hBOOL(hAPP(hAPP(X53,X50),X52))
| ~ c_ListOrder_Ostep1(X53,c_List_Olist_OCons(X50,X49,X54),c_List_Olist_OCons(X52,X51,X54),X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_370])])]) ).
fof(c_0_646_647,plain,
! [X59,X60,X61,X62,X63] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X62,X63),X61),X59))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X62,X63),X60),X59))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X62,X63),X61),X60)) ),
inference(variable_rename,[status(thm)],[c_0_371]) ).
fof(c_0_647_648,plain,
! [X49,X50,X51,X52,X53,X54] :
( X52 = X50
| X51 = X49
| ~ c_ListOrder_Ostep1(X53,c_List_Olist_OCons(X50,X49,X54),c_List_Olist_OCons(X52,X51,X54),X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_372])])]) ).
fof(c_0_648_649,plain,
! [X62,X63,X64,X65,X66] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X66)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),X65),X64)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),X63),X62)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),X65),X63)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),X64),X62)) ),
inference(variable_rename,[status(thm)],[c_0_373]) ).
fof(c_0_649_650,plain,
! [X40,X41,X42,X43] :
( ~ class_Orderings_Olinorder(X43)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X41,X40,X43),X43)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X42,c_List_Olist_OCons(X41,X40,X43),X43),X43) ),
inference(variable_rename,[status(thm)],[c_0_374]) ).
fof(c_0_650_651,plain,
! [X64,X65,X66,X67,X68] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X64,X68,X67),X66),X65))
| ~ hBOOL(hAPP(hAPP(X64,X65),X66)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_375])])]) ).
fof(c_0_651_652,plain,
! [X64,X65,X66,X67,X68] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X64,X68,X67),X65),X66))
| ~ hBOOL(hAPP(hAPP(X64,X66),X65)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_376])])]) ).
fof(c_0_652_653,plain,
! [X41,X42,X43] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X41),X43)),hAPP(hAPP(c_Lambda_OdB_OApp,X41),X42)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X43),X42)) ),
inference(variable_rename,[status(thm)],[c_0_377]) ).
fof(c_0_653_654,plain,
! [X41,X42,X43] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X43),X41)),hAPP(hAPP(c_Lambda_OdB_OApp,X42),X41)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X43),X42)) ),
inference(variable_rename,[status(thm)],[c_0_378]) ).
fof(c_0_654_655,plain,
! [X48,X49,X50,X51,X52] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X48,X52),X51),X49))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X48,X52),X50),X49))
| ~ hBOOL(hAPP(hAPP(X48,X51),X50)) ),
inference(variable_rename,[status(thm)],[c_0_379]) ).
fof(c_0_655_656,plain,
! [X48,X49,X50,X51,X52] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X48,X52),X51),X49))
| ~ hBOOL(hAPP(hAPP(X48,X50),X49))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X48,X52),X51),X50)) ),
inference(variable_rename,[status(thm)],[c_0_380]) ).
fof(c_0_656_657,plain,
! [X40,X41,X42,X43,X44] :
( ~ hBOOL(hAPP(hAPP(X43,X40),X41))
| c_ListOrder_Ostep1(X43,c_List_Olist_OCons(X40,X42,X44),c_List_Olist_OCons(X41,X42,X44),X44) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_381])])]) ).
fof(c_0_657_658,plain,
! [X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X22,X23)),c_Lambda_Olift(X21,X23)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X22),X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_382])])]) ).
fof(c_0_658_659,plain,
! [X49,X50,X51,X52,X53] :
( c_List_Oappend(X51,c_List_Olist_OCons(X52,c_List_Olist_ONil(X53),X53),X53) != c_List_Oappend(X49,c_List_Olist_OCons(X50,c_List_Olist_ONil(X53),X53),X53)
| X51 = X49 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_383])])]) ).
fof(c_0_659_660,plain,
! [X49,X50,X51,X52,X53] :
( c_List_Oappend(X51,c_List_Olist_OCons(X52,c_List_Olist_ONil(X53),X53),X53) != c_List_Oappend(X49,c_List_Olist_OCons(X50,c_List_Olist_ONil(X53),X53),X53)
| X52 = X50 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_384])])]) ).
fof(c_0_660_661,plain,
! [X46,X47] :
( hBOOL(hAPP(X47,X46))
| ~ hBOOL(hAPP(X47,c_List_Olist_OCons(v_sko__List__Xconcat__Xinduct__1(X47),v_sko__List__Xconcat__Xinduct__2(X47),t_a)))
| ~ hBOOL(hAPP(X47,c_List_Olist_ONil(t_a))) ),
inference(variable_rename,[status(thm)],[c_0_385]) ).
fof(c_0_661_662,plain,
! [X46,X47] :
( hBOOL(hAPP(X47,X46))
| ~ hBOOL(hAPP(X47,c_List_Olist_OCons(v_sko__List__Xtake__Xinduct__1(X47),v_sko__List__Xtake__Xinduct__2(X47),t_a)))
| ~ hBOOL(hAPP(X47,c_List_Olist_ONil(t_a))) ),
inference(variable_rename,[status(thm)],[c_0_386]) ).
fof(c_0_662_663,plain,
! [X46,X47] :
( hBOOL(hAPP(X47,X46))
| ~ hBOOL(hAPP(X47,c_List_Olist_OCons(v_sko__List__Xmap__Xinduct__1(X47),v_sko__List__Xmap__Xinduct__2(X47),t_a)))
| ~ hBOOL(hAPP(X47,c_List_Olist_ONil(t_a))) ),
inference(variable_rename,[status(thm)],[c_0_387]) ).
fof(c_0_663_664,plain,
! [X46,X47] :
( hBOOL(hAPP(X47,X46))
| ~ hBOOL(hAPP(X47,c_List_Olist_OCons(v_sko__List__Xlist__Xinduct__1(X47),v_sko__List__Xlist__Xinduct__2(X47),t_a)))
| ~ hBOOL(hAPP(X47,c_List_Olist_ONil(t_a))) ),
inference(variable_rename,[status(thm)],[c_0_388]) ).
fof(c_0_664_665,plain,
! [X46,X47] :
( hBOOL(hAPP(X47,X46))
| ~ hBOOL(hAPP(X47,c_List_Olist_OCons(v_sko__List__XdropWhile__Xinduct__1(X47),v_sko__List__XdropWhile__Xinduct__2(X47),t_a)))
| ~ hBOOL(hAPP(X47,c_List_Olist_ONil(t_a))) ),
inference(variable_rename,[status(thm)],[c_0_389]) ).
fof(c_0_665_666,plain,
! [X46,X47] :
( hBOOL(hAPP(X47,X46))
| ~ hBOOL(hAPP(X47,c_List_Olist_OCons(v_sko__List__Xremove1__Xinduct__1(X47),v_sko__List__Xremove1__Xinduct__2(X47),t_a)))
| ~ hBOOL(hAPP(X47,c_List_Olist_ONil(t_a))) ),
inference(variable_rename,[status(thm)],[c_0_390]) ).
fof(c_0_666_667,plain,
! [X46,X47] :
( hBOOL(hAPP(X47,X46))
| ~ hBOOL(hAPP(X47,c_List_Olist_OCons(v_sko__List__Xdistinct__Xinduct__1(X47),v_sko__List__Xdistinct__Xinduct__2(X47),t_a)))
| ~ hBOOL(hAPP(X47,c_List_Olist_ONil(t_a))) ),
inference(variable_rename,[status(thm)],[c_0_391]) ).
fof(c_0_667_668,plain,
! [X48,X49,X50,X51] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X51)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X49)),X48) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X48)),X49) ),
inference(variable_rename,[status(thm)],[c_0_392]) ).
fof(c_0_668_669,plain,
! [X48,X49,X50,X51] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X51)
| c_HOL_Oord__class_Oless(X50,X49,X51)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X49),X48),X51) ),
inference(variable_rename,[status(thm)],[c_0_393]) ).
fof(c_0_669_670,plain,
! [X48,X49,X50,X51] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X51)
| c_HOL_Oord__class_Oless(X50,X49,X51)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X48),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X48),X49),X51) ),
inference(variable_rename,[status(thm)],[c_0_394]) ).
fof(c_0_670_671,plain,
! [X60,X61] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X61)),c_Lambda_OdB_OAbs(X60)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X61),X60)) ),
inference(variable_rename,[status(thm)],[c_0_395]) ).
fof(c_0_671_672,plain,
! [X62,X63,X64,X65,X66] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X66)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),X65),X63),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X66),X64),X62),X66)
| ~ c_HOL_Oord__class_Oless(X63,X62,X66)
| ~ c_HOL_Oord__class_Oless(X65,X64,X66) ),
inference(variable_rename,[status(thm)],[c_0_396]) ).
fof(c_0_672_673,plain,
! [X48,X49,X50,X51] :
( c_Wellfounded_Oaccp(X48,X49,X51)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X48,X51),X49),X50))
| ~ c_Wellfounded_Oaccp(X48,X50,X51) ),
inference(variable_rename,[status(thm)],[c_0_397]) ).
fof(c_0_673_674,plain,
! [X48,X49,X50,X51] :
( c_Wellfounded_Oaccp(X48,X49,X51)
| ~ c_Wellfounded_Oaccp(X48,X50,X51)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X48,X51),X49),X50)) ),
inference(variable_rename,[status(thm)],[c_0_398]) ).
fof(c_0_674_675,plain,
! [X48,X49,X50,X51] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X51)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X49)),X48) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X49),X48)) ),
inference(variable_rename,[status(thm)],[c_0_399]) ).
fof(c_0_675_676,plain,
! [X62,X63,X64,X65] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X65)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X65),X64),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X65),X63),X62)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X65),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X65),X64),X63)),X62) ),
inference(variable_rename,[status(thm)],[c_0_400]) ).
fof(c_0_676_677,plain,
! [X48,X49,X50,X51] :
( ~ class_OrderedGroup_Oab__semigroup__add(X51)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X49)),X48) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X49),X48)) ),
inference(variable_rename,[status(thm)],[c_0_401]) ).
fof(c_0_677_678,plain,
! [X48,X49,X50,X51] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X51)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X49)),X48) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X49),X48)) ),
inference(variable_rename,[status(thm)],[c_0_402]) ).
fof(c_0_678_679,plain,
! [X59,X60,X61,X62] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X62)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X60),X59)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X60)),X59) ),
inference(variable_rename,[status(thm)],[c_0_403]) ).
fof(c_0_679_680,plain,
! [X65,X66,X67,X68,X69] :
( c_Type_Otyping(X67,hAPP(hAPP(c_Lambda_OdB_OApp,X66),X65),X68)
| ~ c_Type_Otyping(X67,X65,X69)
| ~ c_Type_Otyping(X67,X66,hAPP(hAPP(c_Type_Otype_OFun,X69),X68)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_404])])]) ).
fof(c_0_680_681,plain,
! [X64,X65,X66,X67] :
( c_List_Omap(X65,X64,X66,X67) != c_List_Olist_ONil(X67)
| X64 = c_List_Olist_ONil(X66) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_405])])]) ).
fof(c_0_681_682,plain,
! [X64,X65,X66,X67] :
( c_List_Olist_ONil(X67) != c_List_Omap(X65,X64,X66,X67)
| X64 = c_List_Olist_ONil(X66) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_406])])]) ).
fof(c_0_682_683,plain,
! [X45,X46,X47,X48] :
( c_List_Olist__update(X45,X47,X46,X48) != c_List_Olist_ONil(X48)
| X45 = c_List_Olist_ONil(X48) ),
inference(variable_rename,[status(thm)],[c_0_407]) ).
fof(c_0_683_684,plain,
! [X53,X54,X55,X56] :
( c_Type_Otyping(X55,X53,X56)
| ~ c_Type_Otyping(X55,X54,X56)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X54),X53)) ),
inference(variable_rename,[status(thm)],[c_0_408]) ).
fof(c_0_684_685,plain,
! [X59,X60,X61,X62,X63] :
( ~ class_OrderedGroup_Oab__group__add(X63)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X63),X61),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X63),X60),X59)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X63),X60),X62)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X63),X61),X59) = X62 ),
inference(variable_rename,[status(thm)],[c_0_409]) ).
fof(c_0_685_686,plain,
! [X44,X45,X46,X47] :
( c_List_Ofilter(X46,c_List_Olist_OCons(X45,X44,X47),X47) = c_List_Olist_OCons(X45,c_List_Ofilter(X46,X44,X47),X47)
| ~ hBOOL(hAPP(X46,X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_410])])]) ).
fof(c_0_686_687,plain,
! [X48,X49,X50] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X50)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X50),X49),X48),c_HOL_Ozero__class_Ozero(X50),X50)
| ~ c_HOL_Oord__class_Oless(X48,c_HOL_Ozero__class_Ozero(X50),X50)
| ~ c_HOL_Oord__class_Oless(X49,c_HOL_Ozero__class_Ozero(X50),X50) ),
inference(variable_rename,[status(thm)],[c_0_411]) ).
fof(c_0_687_688,plain,
! [X48,X49,X50] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X50)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X50),X49),X48),X50)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X50),X48,X50)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X50),X49,X50) ),
inference(variable_rename,[status(thm)],[c_0_412]) ).
fof(c_0_688_689,plain,
! [X48,X49,X50,X51] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X51)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X49),X48),X51)
| ~ c_HOL_Oord__class_Oless(X50,X49,X51) ),
inference(variable_rename,[status(thm)],[c_0_413]) ).
fof(c_0_689_690,plain,
! [X48,X49,X50,X51] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X51)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X49),X48),X51)
| ~ c_HOL_Oord__class_Oless(X50,X49,X51) ),
inference(variable_rename,[status(thm)],[c_0_414]) ).
fof(c_0_690_691,plain,
! [X48,X49,X50,X51] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X51)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X48),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X48),X49),X51)
| ~ c_HOL_Oord__class_Oless(X50,X49,X51) ),
inference(variable_rename,[status(thm)],[c_0_415]) ).
fof(c_0_691_692,plain,
! [X48,X49,X50,X51] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X51)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X48),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X48),X49),X51)
| ~ c_HOL_Oord__class_Oless(X50,X49,X51) ),
inference(variable_rename,[status(thm)],[c_0_416]) ).
fof(c_0_692_693,plain,
! [X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X22,X23)),c_Lambda_Olift(X21,X23)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X22),X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_417])])]) ).
fof(c_0_693_694,plain,
! [X48,X49,X50,X51] :
( ~ class_Ring__and__Field_Oordered__semidom(X51)
| c_HOL_Oord__class_Oless(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X48),X51)
| ~ c_HOL_Oord__class_Oless(X49,X48,X51)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X51),X50,X51) ),
inference(variable_rename,[status(thm)],[c_0_418]) ).
fof(c_0_694_695,plain,
! [X48,X49,X50,X51,X52] :
( hAPP(hAPP(X48,hAPP(hAPP(X48,X51),X50)),X49) = hAPP(hAPP(X48,X51),hAPP(hAPP(X48,X50),X49))
| ~ c_OrderedGroup_Osemigroup__add(X48,X52) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_419])])]) ).
fof(c_0_695_696,plain,
! [X57,X58,X59,X60] :
( c_List_Olistsp(X59,c_List_Oappend(X58,X57,X60),X60)
| ~ c_List_Olistsp(X59,X57,X60)
| ~ c_List_Olistsp(X59,X58,X60) ),
inference(variable_rename,[status(thm)],[c_0_420]) ).
fof(c_0_696_697,plain,
! [X44,X45,X46,X47] :
( c_List_Oremove1(X46,c_List_Olist_OCons(X44,X45,X47),X47) = c_List_Olist_OCons(X44,c_List_Oremove1(X46,X45,X47),X47)
| X46 = X44 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_421])])]) ).
fof(c_0_697_698,plain,
! [X34,X35] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X35)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X35),X34,X35)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X34),X35) ),
inference(variable_rename,[status(thm)],[c_0_422]) ).
fof(c_0_698_699,plain,
! [X34,X35] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X35)
| c_HOL_Oord__class_Oless(X34,c_HOL_Ozero__class_Ozero(X35),X35)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X34),c_HOL_Ozero__class_Ozero(X35),X35) ),
inference(variable_rename,[status(thm)],[c_0_423]) ).
fof(c_0_699_700,plain,
! [X34,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X35)
| c_HOL_Oord__class_Oless(X34,c_HOL_Ozero__class_Ozero(X35),X35)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X34),c_HOL_Ozero__class_Ozero(X35),X35) ),
inference(variable_rename,[status(thm)],[c_0_424]) ).
fof(c_0_700_701,plain,
! [X62,X63,X64,X65] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X65)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X65),X64),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X65),X63),X62)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X65),X63),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X65),X64),X62)) ),
inference(variable_rename,[status(thm)],[c_0_425]) ).
fof(c_0_701_702,plain,
! [X48,X49,X50,X51] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X51)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X49),X48)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X49),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X48)) ),
inference(variable_rename,[status(thm)],[c_0_426]) ).
fof(c_0_702_703,plain,
! [X59,X60,X61,X62] :
( ~ class_OrderedGroup_Oab__group__add(X62)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X60),X59)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X60),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X59)) ),
inference(variable_rename,[status(thm)],[c_0_427]) ).
fof(c_0_703_704,plain,
! [X40,X41,X42,X43] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X42,X43),X41),X40))
| ~ hBOOL(hAPP(hAPP(X42,X41),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_428])])]) ).
fof(c_0_704_705,plain,
! [X57,X58,X59,X60] :
( c_List_Olistsp(X59,X58,X60)
| ~ c_List_Olistsp(X59,c_List_Oappend(X58,X57,X60),X60) ),
inference(variable_rename,[status(thm)],[c_0_429]) ).
fof(c_0_705_706,plain,
! [X57,X58,X59,X60] :
( c_List_Olistsp(X59,X57,X60)
| ~ c_List_Olistsp(X59,c_List_Oappend(X58,X57,X60),X60) ),
inference(variable_rename,[status(thm)],[c_0_430]) ).
fof(c_0_706_707,plain,
! [X25,X26,X27] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X25,c_Lambda_OdB_OVar(X27),X26)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X25)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_431])])]) ).
fof(c_0_707_708,plain,
! [X49,X50,X51,X52] :
( c_List_Orev(X51,X52) != c_List_Olist_OCons(X50,X49,X52)
| X51 = c_List_Oappend(c_List_Orev(X49,X52),c_List_Olist_OCons(X50,c_List_Olist_ONil(X52),X52),X52) ),
inference(variable_rename,[status(thm)],[c_0_432]) ).
fof(c_0_708_709,plain,
! [X40,X41,X42,X43] :
( c_Wellfounded_Oaccp(X41,X40,X43)
| ~ hBOOL(hAPP(hAPP(X41,X40),X42))
| ~ c_Wellfounded_Oaccp(X41,X42,X43) ),
inference(variable_rename,[status(thm)],[c_0_433]) ).
fof(c_0_709_710,plain,
! [X48,X49,X50,X51] :
( c_Wellfounded_Oaccp(X48,X50,X51)
| ~ hBOOL(hAPP(hAPP(X48,X50),X49))
| ~ c_Wellfounded_Oaccp(X48,X49,X51) ),
inference(variable_rename,[status(thm)],[c_0_434]) ).
fof(c_0_710_711,plain,
! [X34,X35] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X35)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X35),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X34),X35)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X35),X34,X35) ),
inference(variable_rename,[status(thm)],[c_0_435]) ).
fof(c_0_711_712,plain,
! [X34,X35] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X35)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X34),c_HOL_Ozero__class_Ozero(X35),X35)
| ~ c_HOL_Oord__class_Oless(X34,c_HOL_Ozero__class_Ozero(X35),X35) ),
inference(variable_rename,[status(thm)],[c_0_436]) ).
fof(c_0_712_713,plain,
! [X34,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X35)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X34),c_HOL_Ozero__class_Ozero(X35),X35)
| ~ c_HOL_Oord__class_Oless(X34,c_HOL_Ozero__class_Ozero(X35),X35) ),
inference(variable_rename,[status(thm)],[c_0_437]) ).
fof(c_0_713_714,plain,
! [X11] :
( hBOOL(hAPP(c_InductTermi_OIT,X11))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X11,tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_438]) ).
fof(c_0_714_715,plain,
! [X32,X33,X34,X35] :
( c_List_Ofilter(X34,c_List_Oreplicate(X33,X32,X35),X35) = c_List_Oreplicate(X33,X32,X35)
| ~ hBOOL(hAPP(X34,X32)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_439])])]) ).
fof(c_0_715_716,plain,
! [X53,X54,X55,X56] :
( c_Type_Otyping(X55,X53,X56)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X54),X53))
| ~ c_Type_Otyping(X55,X54,X56) ),
inference(variable_rename,[status(thm)],[c_0_440]) ).
fof(c_0_716_717,plain,
! [X44,X45,X46,X47] :
( c_List_Oremove1(X45,c_List_Ofilter(X46,X44,X47),X47) = c_List_Ofilter(X46,X44,X47)
| hBOOL(hAPP(X46,X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_441])])]) ).
fof(c_0_717_718,plain,
! [X44,X45,X46,X47] :
( c_List_Ofilter(X46,c_List_Olist_OCons(X45,X44,X47),X47) = c_List_Ofilter(X46,X44,X47)
| hBOOL(hAPP(X46,X45)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_442])])]) ).
fof(c_0_718_719,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Oorder(X62)
| c_HOL_Oord__class_Oless(X59,X61,X62)
| ~ c_HOL_Oord__class_Oless(X59,X60,X62)
| ~ c_HOL_Oord__class_Oless(X60,X61,X62) ),
inference(variable_rename,[status(thm)],[c_0_443]) ).
fof(c_0_719_720,plain,
! [X59,X60,X61,X62] :
( ~ class_Orderings_Opreorder(X62)
| c_HOL_Oord__class_Oless(X61,X59,X62)
| ~ c_HOL_Oord__class_Oless(X60,X59,X62)
| ~ c_HOL_Oord__class_Oless(X61,X60,X62) ),
inference(variable_rename,[status(thm)],[c_0_444]) ).
fof(c_0_720_721,plain,
! [X16,X17] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X17)),c_Lambda_OdB_OAbs(X16)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X17),X16)) ),
inference(variable_rename,[status(thm)],[c_0_445]) ).
fof(c_0_721_722,plain,
! [X44,X45,X46] :
( ~ class_Orderings_Olinorder(X46)
| c_List_Olinorder__class_Osorted(X44,X46)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X45,X44,X46),X46) ),
inference(variable_rename,[status(thm)],[c_0_446]) ).
fof(c_0_722_723,plain,
! [X49,X50,X51] :
( ~ class_Orderings_Olinorder(X51)
| c_List_Olinorder__class_Osorted(X50,X51)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X50,X49,X51),X51) ),
inference(variable_rename,[status(thm)],[c_0_447]) ).
fof(c_0_723_724,plain,
! [X49,X50,X51] :
( ~ class_Orderings_Olinorder(X51)
| c_List_Olinorder__class_Osorted(X49,X51)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X50,X49,X51),X51) ),
inference(variable_rename,[status(thm)],[c_0_448]) ).
fof(c_0_724_725,plain,
! [X49,X50,X51,X52,X53] :
( c_List_Olist_OCons(X51,X50,X53) != c_List_Ofilter(X52,X49,X53)
| hBOOL(hAPP(X52,X51)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_449])])]) ).
fof(c_0_725,plain,
! [X49,X50,X51,X52,X53] :
( c_List_Ofilter(X52,X49,X53) != c_List_Olist_OCons(X51,X50,X53)
| hBOOL(hAPP(X52,X51)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_450])])]) ).
fof(c_0_726,plain,
! [X32,X33,X34,X35] :
( c_List_Ofilter(X34,c_List_Oreplicate(X33,X32,X35),X35) = c_List_Olist_ONil(X35)
| hBOOL(hAPP(X34,X32)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_451])])]) ).
fof(c_0_727,plain,
! [X16] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X16,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X16)) ),
inference(variable_rename,[status(thm)],[c_0_452]) ).
fof(c_0_728,plain,
! [X32,X33,X34] :
( hBOOL(hAPP(hAPP(X34,X32),X33))
| c_HOL_Oord__class_Oless(X32,X33,tc_nat)
| X33 = X32
| c_HOL_Oord__class_Oless(X33,X32,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_453])])]) ).
fof(c_0_729,plain,
! [X59,X60,X61,X62] :
( ~ class_Ring__and__Field_Oidom(X62)
| ~ class_Int_Onumber__ring(X62)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X60) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),X61),X59)
| X60 = X59 ),
inference(variable_rename,[status(thm)],[c_0_454]) ).
fof(c_0_730,plain,
! [X34] :
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X34)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X34)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X34),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
inference(variable_rename,[status(thm)],[c_0_455]) ).
fof(c_0_731,plain,
! [X48,X49,X50] :
( ~ class_Orderings_Oorder(X50)
| ~ c_HOL_Oord__class_Oless(X49,X48,X50)
| ~ c_HOL_Oord__class_Oless(X48,X49,X50) ),
inference(variable_rename,[status(thm)],[c_0_456]) ).
fof(c_0_732,plain,
! [X40,X41,X42] :
( ~ class_Orderings_Olinorder(X42)
| ~ c_HOL_Oord__class_Oless(X41,X40,X42)
| ~ c_HOL_Oord__class_Oless(X40,X41,X42) ),
inference(variable_rename,[status(thm)],[c_0_457]) ).
fof(c_0_733,plain,
! [X40,X41,X42] :
( ~ class_Orderings_Opreorder(X42)
| ~ c_HOL_Oord__class_Oless(X40,X41,X42)
| ~ c_HOL_Oord__class_Oless(X41,X40,X42) ),
inference(variable_rename,[status(thm)],[c_0_458]) ).
fof(c_0_734,plain,
! [X48,X49,X50] :
( ~ class_Orderings_Opreorder(X50)
| ~ c_HOL_Oord__class_Oless(X48,X49,X50)
| ~ c_HOL_Oord__class_Oless(X49,X48,X50) ),
inference(variable_rename,[status(thm)],[c_0_459]) ).
fof(c_0_735,plain,
! [X44,X45,X46] :
( c_List_Olist_OCons(X45,c_List_Olist_ONil(X46),X46) != c_List_Orev(X44,X46)
| X44 = c_List_Olist_OCons(X45,c_List_Olist_ONil(X46),X46) ),
inference(variable_rename,[status(thm)],[c_0_460]) ).
fof(c_0_736,plain,
! [X44,X45,X46] :
( c_List_Orev(X44,X46) != c_List_Olist_OCons(X45,c_List_Olist_ONil(X46),X46)
| X44 = c_List_Olist_OCons(X45,c_List_Olist_ONil(X46),X46) ),
inference(variable_rename,[status(thm)],[c_0_461]) ).
fof(c_0_737,plain,
! [X40,X41,X42,X43,X44] :
( c_List_Oreplicate(X43,X41,X44) != c_List_Oreplicate(X42,X40,X44)
| X41 = X40
| X43 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_462])])]) ).
fof(c_0_738,plain,
! [X40,X41,X42,X43,X44] :
( c_List_Oreplicate(X43,X41,X44) != c_List_Oreplicate(X42,X40,X44)
| X43 = X42 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_463])])]) ).
fof(c_0_739,plain,
! [X48,X49,X50,X51] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X51)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X49) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X48)
| X49 = X48 ),
inference(variable_rename,[status(thm)],[c_0_464]) ).
fof(c_0_740,plain,
! [X48,X49,X50,X51] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X51)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X49) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X50),X48)
| X49 = X48 ),
inference(variable_rename,[status(thm)],[c_0_465]) ).
fof(c_0_741,plain,
! [X48,X49,X50,X51] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X51)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X49),X50) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X51),X48),X50)
| X49 = X48 ),
inference(variable_rename,[status(thm)],[c_0_466]) ).
fof(c_0_742,plain,
! [X49,X50,X51,X52] :
( c_List_Oappend(X50,X51,X52) != c_List_Oappend(X49,X51,X52)
| X50 = X49 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_467])])]) ).
fof(c_0_743,plain,
! [X49,X50,X51,X52] :
( c_List_Oappend(X51,X50,X52) != c_List_Oappend(X51,X49,X52)
| X50 = X49 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_468])])]) ).
fof(c_0_744,plain,
! [X55,X56,X57,X58,X59] :
( c_List_Olist_OCons(X58,X56,X59) != c_List_Olist_OCons(X57,X55,X59)
| X58 = X57 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_469])])]) ).
fof(c_0_745,plain,
! [X55,X56,X57,X58,X59] :
( c_List_Olist_OCons(X58,X56,X59) != c_List_Olist_OCons(X57,X55,X59)
| X56 = X55 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_470])])]) ).
fof(c_0_746,plain,
! [X27,X28] :
( c_HOL_Oord__class_Oless(X27,X27,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X27),X28,X27) = c_Lambda_Oliftn(X27,X28,c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_471])])]) ).
fof(c_0_747,plain,
! [X4,X5,X6] :
( X5 = X4
| ~ hBOOL(hAPP(hAPP(c_fequal(X6),X5),X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_472])])]) ).
fof(c_0_748,plain,
! [X34] :
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X34)))
| X34 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X34))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X34),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X34)) ),
inference(variable_rename,[status(thm)],[c_0_473]) ).
fof(c_0_749,plain,
! [X44,X45,X46] :
( ~ class_Orderings_Olinorder(X46)
| c_List_Olinorder__class_Osorted(c_List_Oremove1(X45,X44,X46),X46)
| ~ c_List_Olinorder__class_Osorted(X44,X46) ),
inference(variable_rename,[status(thm)],[c_0_474]) ).
fof(c_0_750,plain,
! [X41,X42,X43] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X42),X41,X43) = c_Lambda_OdB_OVar(X42)
| ~ c_HOL_Oord__class_Oless(X42,X43,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_475]) ).
fof(c_0_751,plain,
! [X45,X46,X47] :
( c_Lambda_Oliftn(X45,c_Lambda_OdB_OVar(X47),X46) = c_Lambda_OdB_OVar(X47)
| ~ c_HOL_Oord__class_Oless(X47,X46,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_476]) ).
fof(c_0_752,plain,
! [X27,X28] :
( ~ class_Orderings_Olinorder(X28)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X27,c_List_Olist_ONil(X28),X28),X28) ),
inference(variable_rename,[status(thm)],[c_0_477]) ).
fof(c_0_753,plain,
! [X46,X47] :
( hBOOL(hAPP(X47,X46))
| hBOOL(hAPP(X47,v_sko__List__XdropWhile__Xinduct__2(X47)))
| ~ hBOOL(hAPP(X47,c_List_Olist_ONil(t_a))) ),
inference(variable_rename,[status(thm)],[c_0_478]) ).
fof(c_0_754,plain,
! [X46,X47] :
( hBOOL(hAPP(X47,X46))
| hBOOL(hAPP(X47,v_sko__List__Xtake__Xinduct__2(X47)))
| ~ hBOOL(hAPP(X47,c_List_Olist_ONil(t_a))) ),
inference(variable_rename,[status(thm)],[c_0_479]) ).
fof(c_0_755,plain,
! [X46,X47] :
( hBOOL(hAPP(X47,X46))
| hBOOL(hAPP(X47,v_sko__List__Xconcat__Xinduct__2(X47)))
| ~ hBOOL(hAPP(X47,c_List_Olist_ONil(t_a))) ),
inference(variable_rename,[status(thm)],[c_0_480]) ).
fof(c_0_756,plain,
! [X46,X47] :
( hBOOL(hAPP(X47,X46))
| hBOOL(hAPP(X47,v_sko__List__Xdistinct__Xinduct__2(X47)))
| ~ hBOOL(hAPP(X47,c_List_Olist_ONil(t_a))) ),
inference(variable_rename,[status(thm)],[c_0_481]) ).
fof(c_0_757,plain,
! [X46,X47] :
( hBOOL(hAPP(X47,X46))
| hBOOL(hAPP(X47,v_sko__List__Xremove1__Xinduct__2(X47)))
| ~ hBOOL(hAPP(X47,c_List_Olist_ONil(t_a))) ),
inference(variable_rename,[status(thm)],[c_0_482]) ).
fof(c_0_758,plain,
! [X46,X47] :
( hBOOL(hAPP(X47,X46))
| hBOOL(hAPP(X47,v_sko__List__Xlist__Xinduct__2(X47)))
| ~ hBOOL(hAPP(X47,c_List_Olist_ONil(t_a))) ),
inference(variable_rename,[status(thm)],[c_0_483]) ).
fof(c_0_759,plain,
! [X46,X47] :
( hBOOL(hAPP(X47,X46))
| hBOOL(hAPP(X47,v_sko__List__Xmap__Xinduct__2(X47)))
| ~ hBOOL(hAPP(X47,c_List_Olist_ONil(t_a))) ),
inference(variable_rename,[status(thm)],[c_0_484]) ).
fof(c_0_760,plain,
! [X39,X40,X41,X42] :
( hAPP(hAPP(X40,X41),X39) = X41
| ~ c_OrderedGroup_Omonoid__add(X39,X40,X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_485])])]) ).
fof(c_0_761,plain,
! [X39,X40,X41,X42] :
( hAPP(hAPP(X40,X39),X41) = X41
| ~ c_OrderedGroup_Omonoid__add(X39,X40,X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_486])])]) ).
fof(c_0_762,plain,
! [X21,X22] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X21,X22)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_487])])]) ).
fof(c_0_763,plain,
! [X45,X46,X47] :
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X47),X45,X46) = c_Lambda_OdB_OVar(X47)
| X47 = X46
| c_HOL_Oord__class_Oless(X46,X47,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_488]) ).
fof(c_0_764,plain,
! [X45,X46,X47] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X47),X45,X46) = c_Lambda_OdB_OVar(X47)
| X47 = X46
| c_HOL_Oord__class_Oless(X46,X47,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_489]) ).
fof(c_0_765,plain,
! [X44,X45] :
( c_Nat_Osize__class_Osize(c_List_Oremdups(X44,X45),tc_List_Olist(X45)) != c_Nat_Osize__class_Osize(X44,tc_List_Olist(X45))
| c_List_Oremdups(X44,X45) = X44 ),
inference(variable_rename,[status(thm)],[c_0_490]) ).
fof(c_0_766,plain,
! [X40,X41,X42] :
( ~ class_Ring__and__Field_Oordered__idom(X42)
| c_HOL_Oord__class_Oless(X40,X41,X42)
| c_HOL_Oord__class_Oless(X41,X40,X42)
| X41 = X40 ),
inference(variable_rename,[status(thm)],[c_0_491]) ).
fof(c_0_767,plain,
! [X40,X41,X42] :
( ~ class_Orderings_Olinorder(X42)
| X41 = X40
| c_HOL_Oord__class_Oless(X40,X41,X42)
| c_HOL_Oord__class_Oless(X41,X40,X42) ),
inference(variable_rename,[status(thm)],[c_0_492]) ).
fof(c_0_768,plain,
! [X40,X41,X42] :
( ~ class_Orderings_Olinorder(X42)
| c_HOL_Oord__class_Oless(X40,X41,X42)
| c_HOL_Oord__class_Oless(X41,X40,X42)
| X41 = X40 ),
inference(variable_rename,[status(thm)],[c_0_493]) ).
fof(c_0_769,plain,
! [X40,X41,X42] :
( ~ class_Orderings_Olinorder(X42)
| c_HOL_Oord__class_Oless(X40,X41,X42)
| X41 = X40
| c_HOL_Oord__class_Oless(X41,X40,X42) ),
inference(variable_rename,[status(thm)],[c_0_494]) ).
fof(c_0_770,plain,
! [X40,X41,X42] :
( ~ class_Orderings_Olinorder(X42)
| X41 = X40
| c_HOL_Oord__class_Oless(X41,X40,X42)
| c_HOL_Oord__class_Oless(X40,X41,X42) ),
inference(variable_rename,[status(thm)],[c_0_495]) ).
fof(c_0_771,plain,
! [X69,X70,X71,X72] :
( hAPP(hAPP(c_Type_Otype_OFun,X72),X70) != hAPP(hAPP(c_Type_Otype_OFun,X71),X69)
| X70 = X69 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_496])])]) ).
fof(c_0_772,plain,
! [X69,X70,X71,X72] :
( hAPP(hAPP(c_Type_Otype_OFun,X72),X70) != hAPP(hAPP(c_Type_Otype_OFun,X71),X69)
| X72 = X71 ),
inference(variable_rename,[status(thm)],[c_0_497]) ).
fof(c_0_773,plain,
! [X15,X16,X17,X18] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X18),X16) != hAPP(hAPP(c_Lambda_OdB_OApp,X17),X15)
| X18 = X17 ),
inference(variable_rename,[status(thm)],[c_0_498]) ).
fof(c_0_774,plain,
! [X15,X16,X17,X18] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X18),X16) != hAPP(hAPP(c_Lambda_OdB_OApp,X17),X15)
| X16 = X15 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_499])])]) ).
fof(c_0_775,plain,
! [X27,X28] :
( c_HOL_Oord__class_Oless(X27,X27,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X27),X28,X27) = X28 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_500])])]) ).
fof(c_0_776,plain,
! [X47,X48,X49] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X49)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X47) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X48) ),
inference(variable_rename,[status(thm)],[c_0_501]) ).
fof(c_0_777,plain,
! [X48,X49,X50] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X50)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X50),X49),X48) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X50),X48),X49) ),
inference(variable_rename,[status(thm)],[c_0_502]) ).
fof(c_0_778,plain,
! [X40,X41,X42] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X42)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X42),X41),X40) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X42),X40),X41) ),
inference(variable_rename,[status(thm)],[c_0_503]) ).
fof(c_0_779,plain,
! [X24,X25,X26] :
( hAPP(X25,X24) = X26
| ~ c_Type_Otyping(X25,c_Lambda_OdB_OVar(X24),X26) ),
inference(variable_rename,[status(thm)],[c_0_504]) ).
fof(c_0_780,plain,
! [X18,X19] :
( c_HOL_Oord__class_Oless(X18,X19,tc_nat)
| c_HOL_Oord__class_Oless(X19,X18,tc_nat)
| X19 = X18 ),
inference(variable_rename,[status(thm)],[c_0_505]) ).
fof(c_0_781,plain,
! [X40,X41] :
( c_HOL_Oord__class_Oless(X40,X41,tc_nat)
| c_HOL_Oord__class_Oless(X41,X40,tc_nat)
| X41 = X40 ),
inference(variable_rename,[status(thm)],[c_0_506]) ).
fof(c_0_782,plain,
! [X45,X46] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X46),X45) = c_Lambda_OdB_OVar(X46)
| ~ c_HOL_Oord__class_Oless(X46,X45,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_507]) ).
fof(c_0_783,plain,
! [X34,X35,X36] :
( ~ class_Ring__and__Field_Oidom(X36)
| ~ class_Int_Onumber__ring(X36)
| X34 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X36),X34),X35)
| X35 = c_HOL_Ozero__class_Ozero(X36) ),
inference(variable_rename,[status(thm)],[c_0_508]) ).
fof(c_0_784,plain,
! [X34,X35] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X35)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),X34) != c_HOL_Ozero__class_Ozero(X35)
| X34 = c_HOL_Ozero__class_Ozero(X35) ),
inference(variable_rename,[status(thm)],[c_0_509]) ).
fof(c_0_785,plain,
! [X44,X45] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X44,tc_List_Olist(X45)),tc_nat)
| X44 = c_List_Olist_ONil(X45) ),
inference(variable_rename,[status(thm)],[c_0_510]) ).
fof(c_0_786,plain,
! [X44,X45,X46] :
( c_List_Orotate(X45,X44,X46) != c_List_Olist_ONil(X46)
| X44 = c_List_Olist_ONil(X46) ),
inference(variable_rename,[status(thm)],[c_0_511]) ).
fof(c_0_787,plain,
! [X49,X50,X51] :
( c_List_Oappend(X50,X49,X51) != c_List_Olist_ONil(X51)
| X49 = c_List_Olist_ONil(X51) ),
inference(variable_rename,[status(thm)],[c_0_512]) ).
fof(c_0_788,plain,
! [X49,X50,X51] :
( c_List_Oappend(X50,X49,X51) != c_List_Olist_ONil(X51)
| X50 = c_List_Olist_ONil(X51) ),
inference(variable_rename,[status(thm)],[c_0_513]) ).
fof(c_0_789,plain,
! [X49,X50,X51] :
( c_List_Olist_ONil(X51) != c_List_Oappend(X50,X49,X51)
| X49 = c_List_Olist_ONil(X51) ),
inference(variable_rename,[status(thm)],[c_0_514]) ).
fof(c_0_790,plain,
! [X49,X50,X51] :
( c_List_Olist_ONil(X51) != c_List_Oappend(X50,X49,X51)
| X50 = c_List_Olist_ONil(X51) ),
inference(variable_rename,[status(thm)],[c_0_515]) ).
fof(c_0_791,plain,
! [X27,X28,X29] :
( c_List_Oreplicate(X28,X27,X29) != c_List_Olist_ONil(X29)
| X28 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_516])])]) ).
fof(c_0_792,plain,
! [X27,X28,X29] :
( c_List_Olist_ONil(X29) != c_List_Oreplicate(X28,X27,X29)
| X28 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_517])])]) ).
fof(c_0_793,plain,
! [X27,X28] :
( ~ class_Orderings_Oorder(X28)
| ~ c_HOL_Oord__class_Oless(X27,X27,X28) ),
inference(variable_rename,[status(thm)],[c_0_518]) ).
fof(c_0_794,plain,
! [X27,X28] :
( ~ class_Orderings_Olinorder(X28)
| ~ c_HOL_Oord__class_Oless(X27,X27,X28) ),
inference(variable_rename,[status(thm)],[c_0_519]) ).
fof(c_0_795,plain,
! [X27,X28] :
( ~ class_Orderings_Opreorder(X28)
| ~ c_HOL_Oord__class_Oless(X27,X27,X28) ),
inference(variable_rename,[status(thm)],[c_0_520]) ).
fof(c_0_796,plain,
! [X49,X50,X51] :
( X49 != c_List_Oappend(X50,X49,X51)
| X50 = c_List_Olist_ONil(X51) ),
inference(variable_rename,[status(thm)],[c_0_521]) ).
fof(c_0_797,plain,
! [X49,X50,X51] :
( c_List_Oappend(X50,X49,X51) != X49
| X50 = c_List_Olist_ONil(X51) ),
inference(variable_rename,[status(thm)],[c_0_522]) ).
fof(c_0_798,plain,
! [X49,X50,X51] :
( X50 != c_List_Oappend(X50,X49,X51)
| X49 = c_List_Olist_ONil(X51) ),
inference(variable_rename,[status(thm)],[c_0_523]) ).
fof(c_0_799,plain,
! [X49,X50,X51] :
( c_List_Oappend(X50,X49,X51) != X50
| X49 = c_List_Olist_ONil(X51) ),
inference(variable_rename,[status(thm)],[c_0_524]) ).
fof(c_0_800,plain,
! [X44,X45] :
( c_List_Oremdups(X44,X45) != X44
| c_Nat_Osize__class_Osize(c_List_Oremdups(X44,X45),tc_List_Olist(X45)) = c_Nat_Osize__class_Osize(X44,tc_List_Olist(X45)) ),
inference(variable_rename,[status(thm)],[c_0_525]) ).
fof(c_0_801,plain,
! [X11] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X11)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X11)) ),
inference(variable_rename,[status(thm)],[c_0_526]) ).
fof(c_0_802,plain,
! [X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4)) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_527]) ).
fof(c_0_803,plain,
! [X27,X28] :
( ~ class_Ring__and__Field_Oidom(X28)
| ~ class_Int_Onumber__ring(X28)
| X27 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),c_HOL_Ozero__class_Ozero(X28)) ),
inference(variable_rename,[status(thm)],[c_0_528]) ).
fof(c_0_804,plain,
! [X27,X28] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),c_HOL_Ozero__class_Ozero(X28)),X27) = X27 ),
inference(variable_rename,[status(thm)],[c_0_529]) ).
fof(c_0_805,plain,
! [X34,X35] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X35)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),c_HOL_Ozero__class_Ozero(X35)),X34) = X34 ),
inference(variable_rename,[status(thm)],[c_0_530]) ).
fof(c_0_806,plain,
! [X34,X35] :
( ~ class_OrderedGroup_Omonoid__add(X35)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),c_HOL_Ozero__class_Ozero(X35)),X34) = X34 ),
inference(variable_rename,[status(thm)],[c_0_531]) ).
fof(c_0_807,plain,
! [X34,X35] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),c_HOL_Ozero__class_Ozero(X35)),X34) = X34 ),
inference(variable_rename,[status(thm)],[c_0_532]) ).
fof(c_0_808,plain,
! [X50,X51] :
( ~ class_Orderings_Olinorder(X51)
| c_List_Olinorder__class_Osorted(c_List_Oremdups(X50,X51),X51)
| ~ c_List_Olinorder__class_Osorted(X50,X51) ),
inference(variable_rename,[status(thm)],[c_0_533]) ).
fof(c_0_809,plain,
! [X34,X35] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X35)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),c_HOL_Ozero__class_Ozero(X35)) = X34 ),
inference(variable_rename,[status(thm)],[c_0_534]) ).
fof(c_0_810,plain,
! [X34,X35] :
( ~ class_OrderedGroup_Omonoid__add(X35)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),c_HOL_Ozero__class_Ozero(X35)) = X34 ),
inference(variable_rename,[status(thm)],[c_0_535]) ).
fof(c_0_811,plain,
! [X34,X35] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X35)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X35),X34),c_HOL_Ozero__class_Ozero(X35)) = X34 ),
inference(variable_rename,[status(thm)],[c_0_536]) ).
fof(c_0_812,plain,
! [X18] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_nat)
| X18 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_537]) ).
fof(c_0_813,plain,
! [X49,X50,X51] :
( c_List_Orev(X50,X51) != c_List_Orev(X49,X51)
| X50 = X49 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_538])])]) ).
fof(c_0_814,plain,
! [X44,X45] :
( c_Nat_Osize__class_Osize(X44,tc_List_Olist(X45)) != c_HOL_Ozero__class_Ozero(tc_nat)
| X44 = c_List_Olist_ONil(X45) ),
inference(variable_rename,[status(thm)],[c_0_539]) ).
fof(c_0_815,plain,
! [X6,X7] :
( class_Orderings_Opreorder(tc_fun(X6,X7))
| ~ class_Orderings_Opreorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_540]) ).
fof(c_0_816,plain,
! [X6,X7] :
( class_Orderings_Oorder(tc_fun(X6,X7))
| ~ class_Orderings_Oorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_541]) ).
fof(c_0_817,plain,
! [X27,X28] :
( c_List_Oremdups(X27,X28) != c_List_Olist_ONil(X28)
| X27 = c_List_Olist_ONil(X28) ),
inference(variable_rename,[status(thm)],[c_0_542]) ).
fof(c_0_818,plain,
! [X44,X45] :
( c_List_Olist_ONil(X45) != c_List_Orev(X44,X45)
| X44 = c_List_Olist_ONil(X45) ),
inference(variable_rename,[status(thm)],[c_0_543]) ).
fof(c_0_819,plain,
! [X27,X28] :
( c_List_Olist_ONil(X28) != c_List_Oremdups(X27,X28)
| X27 = c_List_Olist_ONil(X28) ),
inference(variable_rename,[status(thm)],[c_0_544]) ).
fof(c_0_820,plain,
! [X44,X45] :
( c_List_Orev(X44,X45) != c_List_Olist_ONil(X45)
| X44 = c_List_Olist_ONil(X45) ),
inference(variable_rename,[status(thm)],[c_0_545]) ).
fof(c_0_821,plain,
! [X4] :
( ~ class_OrderedGroup_Osemigroup__add(X4)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_546]) ).
fof(c_0_822,plain,
! [X4] :
( ~ class_Orderings_Olinorder(X4)
| c_List_Olinorder__class_Osorted(c_List_Olist_ONil(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_547]) ).
fof(c_0_823,plain,
! [X58,X59] :
( c_Lambda_OdB_OAbs(X59) != c_Lambda_OdB_OAbs(X58)
| X59 = X58 ),
inference(variable_rename,[status(thm)],[c_0_548]) ).
fof(c_0_824,plain,
! [X20,X21] :
( c_Lambda_OdB_OVar(X21) != c_Lambda_OdB_OVar(X20)
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_549]) ).
cnf(c_0_825,plain,
( X7 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(split_conjunct,[status(thm)],[c_0_550]) ).
cnf(c_0_826,plain,
( X3 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_551]) ).
cnf(c_0_827,plain,
( c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(split_conjunct,[status(thm)],[c_0_552]) ).
cnf(c_0_828,plain,
( c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_553]) ).
cnf(c_0_829,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(split_conjunct,[status(thm)],[c_0_554]) ).
cnf(c_0_830,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(split_conjunct,[status(thm)],[c_0_555]) ).
cnf(c_0_831,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_556]) ).
cnf(c_0_832,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_557]) ).
cnf(c_0_833,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_558]) ).
cnf(c_0_834,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_559]) ).
cnf(c_0_835,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_List_Olist_Olist__case(X5,X2,c_List_Olist_OCons(X3,X4,t_b),t_a,t_b))) ),
inference(split_conjunct,[status(thm)],[c_0_560]) ).
cnf(c_0_836,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_List_Olist_Olist__case(X5,X2,c_List_Olist_OCons(X3,X4,t_b),t_a,t_b))) ),
inference(split_conjunct,[status(thm)],[c_0_561]) ).
cnf(c_0_837,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_562]) ).
cnf(c_0_838,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_563]) ).
cnf(c_0_839,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(split_conjunct,[status(thm)],[c_0_564]) ).
cnf(c_0_840,plain,
( hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(split_conjunct,[status(thm)],[c_0_565]) ).
cnf(c_0_841,plain,
( X4 = X5
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
inference(split_conjunct,[status(thm)],[c_0_566]) ).
cnf(c_0_842,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_567]) ).
cnf(c_0_843,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_568]) ).
cnf(c_0_844,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_569]) ).
cnf(c_0_845,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_570]) ).
cnf(c_0_846,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_Olist__case(X2,X3,c_List_Olist_ONil(t_b),t_a,t_b))) ),
inference(split_conjunct,[status(thm)],[c_0_571]) ).
cnf(c_0_847,plain,
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_572]) ).
cnf(c_0_848,plain,
( c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(split_conjunct,[status(thm)],[c_0_573]) ).
cnf(c_0_849,plain,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_850,plain,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(split_conjunct,[status(thm)],[c_0_575]) ).
cnf(c_0_851,plain,
( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_852,plain,
( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_577]) ).
cnf(c_0_853,plain,
( hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_578]) ).
cnf(c_0_854,plain,
( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(X1,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_579]) ).
cnf(c_0_855,plain,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_856,plain,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| X1 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_581]) ).
cnf(c_0_857,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_858,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(split_conjunct,[status(thm)],[c_0_583]) ).
cnf(c_0_859,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_860,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(split_conjunct,[status(thm)],[c_0_585]) ).
cnf(c_0_861,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_586]) ).
cnf(c_0_862,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_587]) ).
cnf(c_0_863,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_588]) ).
cnf(c_0_864,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_589]) ).
cnf(c_0_865,plain,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_590]) ).
cnf(c_0_866,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_591]) ).
cnf(c_0_867,plain,
( c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_592]) ).
cnf(c_0_868,plain,
( hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3)
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_593]) ).
cnf(c_0_869,plain,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1))
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_594]) ).
cnf(c_0_870,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_595]) ).
cnf(c_0_871,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| X2 = c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_596]) ).
cnf(c_0_872,plain,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Oappend(X3,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| X1 != c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_597]) ).
cnf(c_0_873,plain,
( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_598]) ).
cnf(c_0_874,plain,
( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))
| X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_599]) ).
cnf(c_0_875,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| X1 = c_List_Oappend(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X3,X4,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3) != c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_600]) ).
cnf(c_0_876,plain,
( c_Map_Omap__upds(X1,c_List_Oappend(X2,X3,X4),X5,X4,X6) = c_Map_Omap__upds(X1,X2,X5,X4,X6)
| c_Nat_Osize__class_Osize(X2,tc_List_Olist(X4)) != c_Nat_Osize__class_Osize(X5,tc_List_Olist(X6)) ),
inference(split_conjunct,[status(thm)],[c_0_601]) ).
cnf(c_0_877,plain,
( c_Map_Omap__upds(X1,X2,c_List_Oappend(X3,X4,X5),X6,X5) = c_Map_Omap__upds(X1,X2,X3,X6,X5)
| c_Nat_Osize__class_Osize(X2,tc_List_Olist(X6)) != c_Nat_Osize__class_Osize(X3,tc_List_Olist(X5)) ),
inference(split_conjunct,[status(thm)],[c_0_602]) ).
cnf(c_0_878,plain,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_603]) ).
cnf(c_0_879,plain,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_604]) ).
cnf(c_0_880,plain,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_605]) ).
cnf(c_0_881,plain,
( X1 = c_Lambda_OdB_OAbs(X2)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_606]) ).
cnf(c_0_882,plain,
( c_Lambda_OdB_OAbs(X1) = X2
| c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_607]) ).
cnf(c_0_883,plain,
( c_Lambda_OdB_OVar(X1) = X2
| c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_608]) ).
cnf(c_0_884,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_609]) ).
cnf(c_0_885,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
inference(split_conjunct,[status(thm)],[c_0_610]) ).
cnf(c_0_886,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_611]) ).
cnf(c_0_887,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_612]) ).
cnf(c_0_888,plain,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_613]) ).
cnf(c_0_889,plain,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_614]) ).
cnf(c_0_890,plain,
( X3 = X6
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_615]) ).
cnf(c_0_891,plain,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_616]) ).
cnf(c_0_892,plain,
( X1 = X2
| c_List_Olist__update(c_List_Olist__update(X3,X1,X4,X5),X2,X6,X5) = c_List_Olist__update(c_List_Olist__update(X3,X2,X6,X5),X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_617]) ).
cnf(c_0_893,plain,
( X3 = X6
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_618]) ).
cnf(c_0_894,plain,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| X1 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))
| X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_619]) ).
cnf(c_0_895,plain,
( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_620]) ).
cnf(c_0_896,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_621]) ).
cnf(c_0_897,plain,
( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_622]) ).
cnf(c_0_898,plain,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xtypes__snocE__1__1(X4,X1,X3,X2))
| ~ c_Type_Otypings(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X4) ),
inference(split_conjunct,[status(thm)],[c_0_623]) ).
cnf(c_0_899,plain,
( c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtypes__snocE__1__2(X4,X1,X3,X2))
| ~ c_Type_Otypings(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X4) ),
inference(split_conjunct,[status(thm)],[c_0_624]) ).
cnf(c_0_900,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_625]) ).
cnf(c_0_901,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_626]) ).
cnf(c_0_902,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_627]) ).
cnf(c_0_903,plain,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_628]) ).
cnf(c_0_904,plain,
( c_List_Olist__update(c_List_Oappend(X2,X4,X3),X1,X5,X3) = c_List_Oappend(c_List_Olist__update(X2,X1,X5,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_629]) ).
cnf(c_0_905,plain,
( c_List_Olist__update(c_List_Oappend(X2,X4,X3),X1,X5,X3) = c_List_Oappend(c_List_Olist__update(X2,X1,X5,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_630]) ).
cnf(c_0_906,plain,
( c_List_Olistrelp(X1,c_List_Olist_OCons(X2,X4,X6),c_List_Olist_OCons(X3,X5,X6),X6)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_List_Olistrelp(X1,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_631]) ).
cnf(c_0_907,plain,
( X6 = X3
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_632]) ).
cnf(c_0_908,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_633]) ).
cnf(c_0_909,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_634]) ).
cnf(c_0_910,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_635]) ).
cnf(c_0_911,plain,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_636]) ).
cnf(c_0_912,plain,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_637]) ).
cnf(c_0_913,plain,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_638]) ).
cnf(c_0_914,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_639]) ).
cnf(c_0_915,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_640]) ).
cnf(c_0_916,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_641]) ).
cnf(c_0_917,plain,
( c_List_Olist_OCons(X1,c_List_Ofilter(X2,X3,X4),X4) = c_List_Ofilter(X2,c_List_Oappend(X5,c_List_Olist_OCons(X1,X3,X4),X4),X4)
| hBOOL(hAPP(X2,c_List_Osko__List__XCons__eq__filter__iff__1__3(X2,X5,X4)))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_642]) ).
cnf(c_0_918,plain,
( c_List_Ofilter(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,X4,X5),X5),X5) = c_List_Olist_OCons(X3,c_List_Ofilter(X1,X4,X5),X5)
| hBOOL(hAPP(X1,c_List_Osko__List__Xfilter__eq__Cons__iff__1__3(X1,X2,X5)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_643]) ).
cnf(c_0_919,plain,
( c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2))
| c_List_Omap(X4,X1,X2,X5) != c_List_Omap(X4,X3,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_644]) ).
cnf(c_0_920,plain,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_645]) ).
cnf(c_0_921,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_646]) ).
cnf(c_0_922,plain,
( X6 = X3
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_647]) ).
cnf(c_0_923,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_648]) ).
cnf(c_0_924,plain,
( c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X2,X3,X4),X4)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,c_List_Olist_OCons(X2,X3,X4),X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(split_conjunct,[status(thm)],[c_0_649]) ).
cnf(c_0_925,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_650]) ).
cnf(c_0_926,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_651]) ).
cnf(c_0_927,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_652]) ).
cnf(c_0_928,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_653]) ).
cnf(c_0_929,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_654]) ).
cnf(c_0_930,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_655]) ).
cnf(c_0_931,plain,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_656]) ).
cnf(c_0_932,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_657]) ).
cnf(c_0_933,plain,
( X1 = X2
| c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_658]) ).
cnf(c_0_934,plain,
( X1 = X2
| c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_659]) ).
cnf(c_0_935,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xconcat__Xinduct__1(X1),v_sko__List__Xconcat__Xinduct__2(X1),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_660]) ).
cnf(c_0_936,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xtake__Xinduct__1(X1),v_sko__List__Xtake__Xinduct__2(X1),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_661]) ).
cnf(c_0_937,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xmap__Xinduct__1(X1),v_sko__List__Xmap__Xinduct__2(X1),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_662]) ).
cnf(c_0_938,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xlist__Xinduct__1(X1),v_sko__List__Xlist__Xinduct__2(X1),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_663]) ).
cnf(c_0_939,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__XdropWhile__Xinduct__1(X1),v_sko__List__XdropWhile__Xinduct__2(X1),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_664]) ).
cnf(c_0_940,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xremove1__Xinduct__1(X1),v_sko__List__Xremove1__Xinduct__2(X1),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_665]) ).
cnf(c_0_941,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xdistinct__Xinduct__1(X1),v_sko__List__Xdistinct__Xinduct__2(X1),t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_666]) ).
cnf(c_0_942,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_667]) ).
cnf(c_0_943,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_668]) ).
cnf(c_0_944,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_669]) ).
cnf(c_0_945,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_670]) ).
cnf(c_0_946,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_671]) ).
cnf(c_0_947,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_672]) ).
cnf(c_0_948,plain,
( c_Wellfounded_Oaccp(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_673]) ).
cnf(c_0_949,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_674]) ).
cnf(c_0_950,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_675]) ).
cnf(c_0_951,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_676]) ).
cnf(c_0_952,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_677]) ).
cnf(c_0_953,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_678]) ).
cnf(c_0_954,plain,
( c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4)
| ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
| ~ c_Type_Otyping(X1,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_679]) ).
cnf(c_0_955,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
inference(split_conjunct,[status(thm)],[c_0_680]) ).
cnf(c_0_956,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X3) != c_List_Omap(X4,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_681]) ).
cnf(c_0_957,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist__update(X1,X3,X4,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[c_0_682]) ).
cnf(c_0_958,plain,
( c_Type_Otyping(X3,X2,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ c_Type_Otyping(X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_683]) ).
cnf(c_0_959,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_684]) ).
cnf(c_0_960,plain,
( c_List_Ofilter(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Ofilter(X1,X3,X4),X4)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_685]) ).
cnf(c_0_961,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_686]) ).
cnf(c_0_962,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_687]) ).
cnf(c_0_963,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_688]) ).
cnf(c_0_964,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_689]) ).
cnf(c_0_965,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_690]) ).
cnf(c_0_966,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(split_conjunct,[status(thm)],[c_0_691]) ).
cnf(c_0_967,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_692]) ).
cnf(c_0_968,plain,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_693]) ).
cnf(c_0_969,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_694]) ).
cnf(c_0_970,plain,
( c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| ~ c_List_Olistsp(X1,X2,X3)
| ~ c_List_Olistsp(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_695]) ).
cnf(c_0_971,plain,
( X1 = X2
| c_List_Oremove1(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Oremove1(X1,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_696]) ).
cnf(c_0_972,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_697]) ).
cnf(c_0_973,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_698]) ).
cnf(c_0_974,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_699]) ).
cnf(c_0_975,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_700]) ).
cnf(c_0_976,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_701]) ).
cnf(c_0_977,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_702]) ).
cnf(c_0_978,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_703]) ).
cnf(c_0_979,plain,
( c_List_Olistsp(X1,X2,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_704]) ).
cnf(c_0_980,plain,
( c_List_Olistsp(X1,X3,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_705]) ).
cnf(c_0_981,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_706]) ).
cnf(c_0_982,plain,
( X1 = c_List_Oappend(c_List_Orev(X2,X3),c_List_Olist_OCons(X4,c_List_Olist_ONil(X3),X3),X3)
| c_List_Orev(X1,X3) != c_List_Olist_OCons(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_707]) ).
cnf(c_0_983,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_708]) ).
cnf(c_0_984,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_709]) ).
cnf(c_0_985,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_710]) ).
cnf(c_0_986,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_711]) ).
cnf(c_0_987,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_712]) ).
cnf(c_0_988,plain,
( hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
inference(split_conjunct,[status(thm)],[c_0_713]) ).
cnf(c_0_989,plain,
( c_List_Ofilter(X1,c_List_Oreplicate(X3,X2,X4),X4) = c_List_Oreplicate(X3,X2,X4)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_714]) ).
cnf(c_0_990,plain,
( c_Type_Otyping(X1,X4,X3)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_715]) ).
cnf(c_0_991,plain,
( hBOOL(hAPP(X1,X2))
| c_List_Oremove1(X2,c_List_Ofilter(X1,X3,X4),X4) = c_List_Ofilter(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_716]) ).
cnf(c_0_992,plain,
( hBOOL(hAPP(X1,X2))
| c_List_Ofilter(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Ofilter(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_717]) ).
cnf(c_0_993,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_718]) ).
cnf(c_0_994,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_719]) ).
cnf(c_0_995,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_720]) ).
cnf(c_0_996,plain,
( c_List_Olinorder__class_Osorted(X2,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_721]) ).
cnf(c_0_997,plain,
( c_List_Olinorder__class_Osorted(X1,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X1,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_722]) ).
cnf(c_0_998,plain,
( c_List_Olinorder__class_Osorted(X2,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X1,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_723]) ).
cnf(c_0_999,plain,
( hBOOL(hAPP(X1,X2))
| c_List_Olist_OCons(X2,X3,X4) != c_List_Ofilter(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_724]) ).
cnf(c_0_1000,plain,
( hBOOL(hAPP(X1,X2))
| c_List_Ofilter(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_725]) ).
cnf(c_0_1001,plain,
( hBOOL(hAPP(X1,X2))
| c_List_Ofilter(X1,c_List_Oreplicate(X3,X2,X4),X4) = c_List_Olist_ONil(X4) ),
inference(split_conjunct,[status(thm)],[c_0_726]) ).
cnf(c_0_1002,plain,
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_727]) ).
cnf(c_0_1003,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_728]) ).
cnf(c_0_1004,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_729]) ).
cnf(c_0_1005,plain,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_730]) ).
cnf(c_0_1006,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_731]) ).
cnf(c_0_1007,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_732]) ).
cnf(c_0_1008,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_733]) ).
cnf(c_0_1009,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_734]) ).
cnf(c_0_1010,plain,
( X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3)
| c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3) != c_List_Orev(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_735]) ).
cnf(c_0_1011,plain,
( X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3)
| c_List_Orev(X1,X3) != c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_736]) ).
cnf(c_0_1012,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_737]) ).
cnf(c_0_1013,plain,
( X1 = X2
| c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_738]) ).
cnf(c_0_1014,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_739]) ).
cnf(c_0_1015,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_740]) ).
cnf(c_0_1016,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_741]) ).
cnf(c_0_1017,plain,
( X1 = X2
| c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_742]) ).
cnf(c_0_1018,plain,
( X1 = X2
| c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_743]) ).
cnf(c_0_1019,plain,
( X1 = X2
| c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_744]) ).
cnf(c_0_1020,plain,
( X1 = X2
| c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_745]) ).
cnf(c_0_1021,plain,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_746]) ).
cnf(c_0_1022,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_747]) ).
cnf(c_0_1023,plain,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| X1 = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_748]) ).
cnf(c_0_1024,plain,
( c_List_Olinorder__class_Osorted(c_List_Oremove1(X3,X1,X2),X2)
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_749]) ).
cnf(c_0_1025,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_750]) ).
cnf(c_0_1026,plain,
( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_751]) ).
cnf(c_0_1027,plain,
( c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_752]) ).
cnf(c_0_1028,plain,
( hBOOL(hAPP(X1,v_sko__List__XdropWhile__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_753]) ).
cnf(c_0_1029,plain,
( hBOOL(hAPP(X1,v_sko__List__Xtake__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_754]) ).
cnf(c_0_1030,plain,
( hBOOL(hAPP(X1,v_sko__List__Xconcat__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_755]) ).
cnf(c_0_1031,plain,
( hBOOL(hAPP(X1,v_sko__List__Xdistinct__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_756]) ).
cnf(c_0_1032,plain,
( hBOOL(hAPP(X1,v_sko__List__Xremove1__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_757]) ).
cnf(c_0_1033,plain,
( hBOOL(hAPP(X1,v_sko__List__Xlist__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_758]) ).
cnf(c_0_1034,plain,
( hBOOL(hAPP(X1,v_sko__List__Xmap__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(split_conjunct,[status(thm)],[c_0_759]) ).
cnf(c_0_1035,plain,
( hAPP(hAPP(X2,X4),X1) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_760]) ).
cnf(c_0_1036,plain,
( hAPP(hAPP(X2,X1),X4) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_761]) ).
cnf(c_0_1037,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_762]) ).
cnf(c_0_1038,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_763]) ).
cnf(c_0_1039,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_764]) ).
cnf(c_0_1040,plain,
( c_List_Oremdups(X1,X2) = X1
| c_Nat_Osize__class_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) != c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_765]) ).
cnf(c_0_1041,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_766]) ).
cnf(c_0_1042,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_767]) ).
cnf(c_0_1043,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_768]) ).
cnf(c_0_1044,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_769]) ).
cnf(c_0_1045,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_770]) ).
cnf(c_0_1046,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_771]) ).
cnf(c_0_1047,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
inference(split_conjunct,[status(thm)],[c_0_772]) ).
cnf(c_0_1048,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
inference(split_conjunct,[status(thm)],[c_0_773]) ).
cnf(c_0_1049,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_774]) ).
cnf(c_0_1050,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_775]) ).
cnf(c_0_1051,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_776]) ).
cnf(c_0_1052,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_777]) ).
cnf(c_0_1053,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_778]) ).
cnf(c_0_1054,plain,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_779]) ).
cnf(c_0_1055,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_780]) ).
cnf(c_0_1056,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_781]) ).
cnf(c_0_1057,plain,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_782]) ).
cnf(c_0_1058,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_783]) ).
cnf(c_0_1059,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_784]) ).
cnf(c_0_1060,plain,
( X1 = c_List_Olist_ONil(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_785]) ).
cnf(c_0_1061,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Orotate(X3,X1,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[c_0_786]) ).
cnf(c_0_1062,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[c_0_787]) ).
cnf(c_0_1063,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[c_0_788]) ).
cnf(c_0_1064,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X2) != c_List_Oappend(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_789]) ).
cnf(c_0_1065,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X2) != c_List_Oappend(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_790]) ).
cnf(c_0_1066,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
inference(split_conjunct,[status(thm)],[c_0_791]) ).
cnf(c_0_1067,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Olist_ONil(X2) != c_List_Oreplicate(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_792]) ).
cnf(c_0_1068,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_793]) ).
cnf(c_0_1069,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_794]) ).
cnf(c_0_1070,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_795]) ).
cnf(c_0_1071,plain,
( X1 = c_List_Olist_ONil(X2)
| X3 != c_List_Oappend(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_796]) ).
cnf(c_0_1072,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_797]) ).
cnf(c_0_1073,plain,
( X1 = c_List_Olist_ONil(X2)
| X3 != c_List_Oappend(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_798]) ).
cnf(c_0_1074,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_799]) ).
cnf(c_0_1075,plain,
( c_Nat_Osize__class_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2))
| c_List_Oremdups(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_800]) ).
cnf(c_0_1076,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_801]) ).
cnf(c_0_1077,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_802]) ).
cnf(c_0_1078,plain,
( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_803]) ).
cnf(c_0_1079,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_804]) ).
cnf(c_0_1080,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_805]) ).
cnf(c_0_1081,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_806]) ).
cnf(c_0_1082,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_807]) ).
cnf(c_0_1083,plain,
( c_List_Olinorder__class_Osorted(c_List_Oremdups(X1,X2),X2)
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_808]) ).
cnf(c_0_1084,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_809]) ).
cnf(c_0_1085,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_810]) ).
cnf(c_0_1086,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_811]) ).
cnf(c_0_1087,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_812]) ).
cnf(c_0_1088,plain,
( X1 = X2
| c_List_Orev(X1,X3) != c_List_Orev(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_813]) ).
cnf(c_0_1089,plain,
( X1 = c_List_Olist_ONil(X2)
| c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_814]) ).
cnf(c_0_1090,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_815]) ).
cnf(c_0_1091,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_816]) ).
cnf(c_0_1092,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oremdups(X1,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[c_0_817]) ).
cnf(c_0_1093,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X2) != c_List_Orev(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_818]) ).
cnf(c_0_1094,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist_ONil(X2) != c_List_Oremdups(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_819]) ).
cnf(c_0_1095,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Orev(X1,X2) != c_List_Olist_ONil(X2) ),
inference(split_conjunct,[status(thm)],[c_0_820]) ).
cnf(c_0_1096,plain,
( c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_821]) ).
cnf(c_0_1097,plain,
( c_List_Olinorder__class_Osorted(c_List_Olist_ONil(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_822]) ).
cnf(c_0_1098,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_823]) ).
cnf(c_0_1099,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_824]) ).
cnf(c_0_1100,plain,
( c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
c_0_825,
[final] ).
cnf(c_0_1101,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB) = X3
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
c_0_826,
[final] ).
cnf(c_0_1102,plain,
( c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
c_0_827,
[final] ).
cnf(c_0_1103,plain,
( c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
c_0_828,
[final] ).
cnf(c_0_1104,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
c_0_829,
[final] ).
cnf(c_0_1105,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
c_0_830,
[final] ).
cnf(c_0_1106,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB) ),
c_0_831,
[final] ).
cnf(c_0_1107,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_832,
[final] ).
cnf(c_0_1108,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_833,
[final] ).
cnf(c_0_1109,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
c_0_834,
[final] ).
cnf(c_0_1110,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_List_Olist_Olist__case(X5,X2,c_List_Olist_OCons(X3,X4,t_b),t_a,t_b))) ),
c_0_835,
[final] ).
cnf(c_0_1111,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_List_Olist_Olist__case(X5,X2,c_List_Olist_OCons(X3,X4,t_b),t_a,t_b))) ),
c_0_836,
[final] ).
cnf(c_0_1112,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
c_0_837,
[final] ).
cnf(c_0_1113,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
c_0_838,
[final] ).
cnf(c_0_1114,plain,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
c_0_839,
[final] ).
cnf(c_0_1115,plain,
( hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
c_0_840,
[final] ).
cnf(c_0_1116,plain,
( X4 = X5
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
c_0_841,
[final] ).
cnf(c_0_1117,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
c_0_842,
[final] ).
cnf(c_0_1118,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
c_0_843,
[final] ).
cnf(c_0_1119,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
c_0_844,
[final] ).
cnf(c_0_1120,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
c_0_845,
[final] ).
cnf(c_0_1121,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_Olist__case(X2,X3,c_List_Olist_ONil(t_b),t_a,t_b))) ),
c_0_846,
[final] ).
cnf(c_0_1122,plain,
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
c_0_847,
[final] ).
cnf(c_0_1123,plain,
( c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
c_0_848,
[final] ).
cnf(c_0_1124,plain,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
c_0_849,
[final] ).
cnf(c_0_1125,plain,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
c_0_850,
[final] ).
cnf(c_0_1126,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_851,
[final] ).
cnf(c_0_1127,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_852,
[final] ).
cnf(c_0_1128,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)
| c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_853,
[final] ).
cnf(c_0_1129,plain,
( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(X1,X5,X3) ),
c_0_854,
[final] ).
cnf(c_0_1130,plain,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_855,
[final] ).
cnf(c_0_1131,plain,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_856,
[final] ).
cnf(c_0_1132,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
c_0_857,
[final] ).
cnf(c_0_1133,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
c_0_858,
[final] ).
cnf(c_0_1134,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
c_0_859,
[final] ).
cnf(c_0_1135,plain,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
c_0_860,
[final] ).
cnf(c_0_1136,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_861,
[final] ).
cnf(c_0_1137,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_862,
[final] ).
cnf(c_0_1138,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_863,
[final] ).
cnf(c_0_1139,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_864,
[final] ).
cnf(c_0_1140,plain,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
c_0_865,
[final] ).
cnf(c_0_1141,plain,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_866,
[final] ).
cnf(c_0_1142,plain,
( c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
c_0_867,
[final] ).
cnf(c_0_1143,plain,
( hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3)
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
c_0_868,
[final] ).
cnf(c_0_1144,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_869,
[final] ).
cnf(c_0_1145,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_870,
[final] ).
cnf(c_0_1146,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_871,
[final] ).
cnf(c_0_1147,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Oappend(X3,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB) != X1 ),
c_0_872,
[final] ).
cnf(c_0_1148,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_873,
[final] ).
cnf(c_0_1149,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_874,
[final] ).
cnf(c_0_1150,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Oappend(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X3,X4,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = X1
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3) != c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_875,
[final] ).
cnf(c_0_1151,plain,
( c_Map_Omap__upds(X1,c_List_Oappend(X2,X3,X4),X5,X4,X6) = c_Map_Omap__upds(X1,X2,X5,X4,X6)
| c_Nat_Osize__class_Osize(X2,tc_List_Olist(X4)) != c_Nat_Osize__class_Osize(X5,tc_List_Olist(X6)) ),
c_0_876,
[final] ).
cnf(c_0_1152,plain,
( c_Map_Omap__upds(X1,X2,c_List_Oappend(X3,X4,X5),X6,X5) = c_Map_Omap__upds(X1,X2,X3,X6,X5)
| c_Nat_Osize__class_Osize(X2,tc_List_Olist(X6)) != c_Nat_Osize__class_Osize(X3,tc_List_Olist(X5)) ),
c_0_877,
[final] ).
cnf(c_0_1153,plain,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_878,
[final] ).
cnf(c_0_1154,plain,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
c_0_879,
[final] ).
cnf(c_0_1155,plain,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_880,
[final] ).
cnf(c_0_1156,plain,
( X1 = c_Lambda_OdB_OAbs(X2)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2) ),
c_0_881,
[final] ).
cnf(c_0_1157,plain,
( c_Lambda_OdB_OAbs(X1) = X2
| c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_882,
[final] ).
cnf(c_0_1158,plain,
( c_Lambda_OdB_OVar(X1) = X2
| c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_883,
[final] ).
cnf(c_0_1159,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_884,
[final] ).
cnf(c_0_1160,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
c_0_885,
[final] ).
cnf(c_0_1161,plain,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_886,
[final] ).
cnf(c_0_1162,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4)) ),
c_0_887,
[final] ).
cnf(c_0_1163,plain,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
c_0_888,
[final] ).
cnf(c_0_1164,plain,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
c_0_889,
[final] ).
cnf(c_0_1165,plain,
( X3 = X6
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
c_0_890,
[final] ).
cnf(c_0_1166,plain,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_891,
[final] ).
cnf(c_0_1167,plain,
( X1 = X2
| c_List_Olist__update(c_List_Olist__update(X3,X1,X4,X5),X2,X6,X5) = c_List_Olist__update(c_List_Olist__update(X3,X2,X6,X5),X1,X4,X5) ),
c_0_892,
[final] ).
cnf(c_0_1168,plain,
( X3 = X6
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
c_0_893,
[final] ).
cnf(c_0_1169,plain,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_894,
[final] ).
cnf(c_0_1170,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_895,
[final] ).
cnf(c_0_1171,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4)) ),
c_0_896,
[final] ).
cnf(c_0_1172,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_897,
[final] ).
cnf(c_0_1173,plain,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xtypes__snocE__1__1(X4,X1,X3,X2))
| ~ c_Type_Otypings(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X4) ),
c_0_898,
[final] ).
cnf(c_0_1174,plain,
( c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtypes__snocE__1__2(X4,X1,X3,X2))
| ~ c_Type_Otypings(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X4) ),
c_0_899,
[final] ).
cnf(c_0_1175,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4)) ),
c_0_900,
[final] ).
cnf(c_0_1176,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_901,
[final] ).
cnf(c_0_1177,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_902,
[final] ).
cnf(c_0_1178,plain,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
c_0_903,
[final] ).
cnf(c_0_1179,plain,
( c_List_Olist__update(c_List_Oappend(X2,X4,X3),X1,X5,X3) = c_List_Oappend(c_List_Olist__update(X2,X1,X5,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
c_0_904,
[final] ).
cnf(c_0_1180,plain,
( c_List_Olist__update(c_List_Oappend(X2,X4,X3),X1,X5,X3) = c_List_Oappend(c_List_Olist__update(X2,X1,X5,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
c_0_905,
[final] ).
cnf(c_0_1181,plain,
( c_List_Olistrelp(X1,c_List_Olist_OCons(X2,X4,X6),c_List_Olist_OCons(X3,X5,X6),X6)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_List_Olistrelp(X1,X4,X5,X6) ),
c_0_906,
[final] ).
cnf(c_0_1182,plain,
( X6 = X3
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
c_0_907,
[final] ).
cnf(c_0_1183,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_908,
[final] ).
cnf(c_0_1184,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
c_0_909,
[final] ).
cnf(c_0_1185,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
c_0_910,
[final] ).
cnf(c_0_1186,plain,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X5,X4) ),
c_0_911,
[final] ).
cnf(c_0_1187,plain,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
c_0_912,
[final] ).
cnf(c_0_1188,plain,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
c_0_913,
[final] ).
cnf(c_0_1189,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_914,
[final] ).
cnf(c_0_1190,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_915,
[final] ).
cnf(c_0_1191,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_916,
[final] ).
cnf(c_0_1192,plain,
( c_List_Ofilter(X2,c_List_Oappend(X5,c_List_Olist_OCons(X1,X3,X4),X4),X4) = c_List_Olist_OCons(X1,c_List_Ofilter(X2,X3,X4),X4)
| hBOOL(hAPP(X2,c_List_Osko__List__XCons__eq__filter__iff__1__3(X2,X5,X4)))
| ~ hBOOL(hAPP(X2,X1)) ),
c_0_917,
[final] ).
cnf(c_0_1193,plain,
( c_List_Ofilter(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,X4,X5),X5),X5) = c_List_Olist_OCons(X3,c_List_Ofilter(X1,X4,X5),X5)
| hBOOL(hAPP(X1,c_List_Osko__List__Xfilter__eq__Cons__iff__1__3(X1,X2,X5)))
| ~ hBOOL(hAPP(X1,X3)) ),
c_0_918,
[final] ).
cnf(c_0_1194,plain,
( c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2))
| c_List_Omap(X4,X1,X2,X5) != c_List_Omap(X4,X3,X2,X5) ),
c_0_919,
[final] ).
cnf(c_0_1195,plain,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
c_0_920,
[final] ).
cnf(c_0_1196,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
c_0_921,
[final] ).
cnf(c_0_1197,plain,
( X6 = X3
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
c_0_922,
[final] ).
cnf(c_0_1198,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_923,
[final] ).
cnf(c_0_1199,plain,
( c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X2,X3,X4),X4)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,c_List_Olist_OCons(X2,X3,X4),X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
c_0_924,
[final] ).
cnf(c_0_1200,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_925,
[final] ).
cnf(c_0_1201,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_926,
[final] ).
cnf(c_0_1202,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_927,
[final] ).
cnf(c_0_1203,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_928,
[final] ).
cnf(c_0_1204,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
c_0_929,
[final] ).
cnf(c_0_1205,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
c_0_930,
[final] ).
cnf(c_0_1206,plain,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X5)) ),
c_0_931,
[final] ).
cnf(c_0_1207,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_932,
[final] ).
cnf(c_0_1208,plain,
( X1 = X2
| c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4) ),
c_0_933,
[final] ).
cnf(c_0_1209,plain,
( X1 = X2
| c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4) ),
c_0_934,
[final] ).
cnf(c_0_1210,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xconcat__Xinduct__1(X1),v_sko__List__Xconcat__Xinduct__2(X1),t_a))) ),
c_0_935,
[final] ).
cnf(c_0_1211,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xtake__Xinduct__1(X1),v_sko__List__Xtake__Xinduct__2(X1),t_a))) ),
c_0_936,
[final] ).
cnf(c_0_1212,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xmap__Xinduct__1(X1),v_sko__List__Xmap__Xinduct__2(X1),t_a))) ),
c_0_937,
[final] ).
cnf(c_0_1213,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xlist__Xinduct__1(X1),v_sko__List__Xlist__Xinduct__2(X1),t_a))) ),
c_0_938,
[final] ).
cnf(c_0_1214,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__XdropWhile__Xinduct__1(X1),v_sko__List__XdropWhile__Xinduct__2(X1),t_a))) ),
c_0_939,
[final] ).
cnf(c_0_1215,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xremove1__Xinduct__1(X1),v_sko__List__Xremove1__Xinduct__2(X1),t_a))) ),
c_0_940,
[final] ).
cnf(c_0_1216,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xdistinct__Xinduct__1(X1),v_sko__List__Xdistinct__Xinduct__2(X1),t_a))) ),
c_0_941,
[final] ).
cnf(c_0_1217,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_942,
[final] ).
cnf(c_0_1218,plain,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_943,
[final] ).
cnf(c_0_1219,plain,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_944,
[final] ).
cnf(c_0_1220,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
c_0_945,
[final] ).
cnf(c_0_1221,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_946,
[final] ).
cnf(c_0_1222,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
c_0_947,
[final] ).
cnf(c_0_1223,plain,
( c_Wellfounded_Oaccp(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
c_0_948,
[final] ).
cnf(c_0_1224,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_949,
[final] ).
cnf(c_0_1225,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_950,
[final] ).
cnf(c_0_1226,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
c_0_951,
[final] ).
cnf(c_0_1227,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_952,
[final] ).
cnf(c_0_1228,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_953,
[final] ).
cnf(c_0_1229,plain,
( c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4)
| ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
| ~ c_Type_Otyping(X1,X5,X3) ),
c_0_954,
[final] ).
cnf(c_0_1230,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
c_0_955,
[final] ).
cnf(c_0_1231,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3) ),
c_0_956,
[final] ).
cnf(c_0_1232,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist__update(X1,X3,X4,X2) != c_List_Olist_ONil(X2) ),
c_0_957,
[final] ).
cnf(c_0_1233,plain,
( c_Type_Otyping(X3,X2,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ c_Type_Otyping(X3,X1,X4) ),
c_0_958,
[final] ).
cnf(c_0_1234,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_959,
[final] ).
cnf(c_0_1235,plain,
( c_List_Ofilter(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Ofilter(X1,X3,X4),X4)
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_960,
[final] ).
cnf(c_0_1236,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_961,
[final] ).
cnf(c_0_1237,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_962,
[final] ).
cnf(c_0_1238,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_963,
[final] ).
cnf(c_0_1239,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_964,
[final] ).
cnf(c_0_1240,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
c_0_965,
[final] ).
cnf(c_0_1241,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
c_0_966,
[final] ).
cnf(c_0_1242,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_967,
[final] ).
cnf(c_0_1243,plain,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_968,
[final] ).
cnf(c_0_1244,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
c_0_969,
[final] ).
cnf(c_0_1245,plain,
( c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| ~ c_List_Olistsp(X1,X2,X3)
| ~ c_List_Olistsp(X1,X4,X3) ),
c_0_970,
[final] ).
cnf(c_0_1246,plain,
( X1 = X2
| c_List_Oremove1(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Oremove1(X1,X3,X4),X4) ),
c_0_971,
[final] ).
cnf(c_0_1247,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_972,
[final] ).
cnf(c_0_1248,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_973,
[final] ).
cnf(c_0_1249,plain,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_974,
[final] ).
cnf(c_0_1250,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_975,
[final] ).
cnf(c_0_1251,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_976,
[final] ).
cnf(c_0_1252,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_977,
[final] ).
cnf(c_0_1253,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_978,
[final] ).
cnf(c_0_1254,plain,
( c_List_Olistsp(X1,X2,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
c_0_979,
[final] ).
cnf(c_0_1255,plain,
( c_List_Olistsp(X1,X3,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
c_0_980,
[final] ).
cnf(c_0_1256,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_981,
[final] ).
cnf(c_0_1257,plain,
( X1 = c_List_Oappend(c_List_Orev(X2,X3),c_List_Olist_OCons(X4,c_List_Olist_ONil(X3),X3),X3)
| c_List_Orev(X1,X3) != c_List_Olist_OCons(X4,X2,X3) ),
c_0_982,
[final] ).
cnf(c_0_1258,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
c_0_983,
[final] ).
cnf(c_0_1259,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
c_0_984,
[final] ).
cnf(c_0_1260,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_985,
[final] ).
cnf(c_0_1261,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_986,
[final] ).
cnf(c_0_1262,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
c_0_987,
[final] ).
cnf(c_0_1263,plain,
( hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
c_0_988,
[final] ).
cnf(c_0_1264,plain,
( c_List_Ofilter(X1,c_List_Oreplicate(X3,X2,X4),X4) = c_List_Oreplicate(X3,X2,X4)
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_989,
[final] ).
cnf(c_0_1265,plain,
( c_Type_Otyping(X1,X4,X3)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
c_0_990,
[final] ).
cnf(c_0_1266,plain,
( hBOOL(hAPP(X1,X2))
| c_List_Oremove1(X2,c_List_Ofilter(X1,X3,X4),X4) = c_List_Ofilter(X1,X3,X4) ),
c_0_991,
[final] ).
cnf(c_0_1267,plain,
( hBOOL(hAPP(X1,X2))
| c_List_Ofilter(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Ofilter(X1,X3,X4) ),
c_0_992,
[final] ).
cnf(c_0_1268,plain,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_993,
[final] ).
cnf(c_0_1269,plain,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_994,
[final] ).
cnf(c_0_1270,plain,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
c_0_995,
[final] ).
cnf(c_0_1271,plain,
( c_List_Olinorder__class_Osorted(X2,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_996,
[final] ).
cnf(c_0_1272,plain,
( c_List_Olinorder__class_Osorted(X1,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X1,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_997,
[final] ).
cnf(c_0_1273,plain,
( c_List_Olinorder__class_Osorted(X2,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X1,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_998,
[final] ).
cnf(c_0_1274,plain,
( hBOOL(hAPP(X1,X2))
| c_List_Olist_OCons(X2,X3,X4) != c_List_Ofilter(X1,X5,X4) ),
c_0_999,
[final] ).
cnf(c_0_1275,plain,
( hBOOL(hAPP(X1,X2))
| c_List_Ofilter(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
c_0_1000,
[final] ).
cnf(c_0_1276,plain,
( hBOOL(hAPP(X1,X2))
| c_List_Ofilter(X1,c_List_Oreplicate(X3,X2,X4),X4) = c_List_Olist_ONil(X4) ),
c_0_1001,
[final] ).
cnf(c_0_1277,plain,
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1002,
[final] ).
cnf(c_0_1278,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
c_0_1003,
[final] ).
cnf(c_0_1279,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_1004,
[final] ).
cnf(c_0_1280,plain,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1005,
[final] ).
cnf(c_0_1281,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1006,
[final] ).
cnf(c_0_1282,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1007,
[final] ).
cnf(c_0_1283,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1008,
[final] ).
cnf(c_0_1284,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1009,
[final] ).
cnf(c_0_1285,plain,
( X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3)
| c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3) != c_List_Orev(X1,X3) ),
c_0_1010,
[final] ).
cnf(c_0_1286,plain,
( X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3)
| c_List_Orev(X1,X3) != c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3) ),
c_0_1011,
[final] ).
cnf(c_0_1287,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
c_0_1012,
[final] ).
cnf(c_0_1288,plain,
( X1 = X2
| c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4) ),
c_0_1013,
[final] ).
cnf(c_0_1289,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
c_0_1014,
[final] ).
cnf(c_0_1290,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
c_0_1015,
[final] ).
cnf(c_0_1291,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
c_0_1016,
[final] ).
cnf(c_0_1292,plain,
( X1 = X2
| c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
c_0_1017,
[final] ).
cnf(c_0_1293,plain,
( X1 = X2
| c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
c_0_1018,
[final] ).
cnf(c_0_1294,plain,
( X1 = X2
| c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
c_0_1019,
[final] ).
cnf(c_0_1295,plain,
( X1 = X2
| c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
c_0_1020,
[final] ).
cnf(c_0_1296,plain,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_1021,
[final] ).
cnf(c_0_1297,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
c_0_1022,
[final] ).
cnf(c_0_1298,plain,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1023,
[final] ).
cnf(c_0_1299,plain,
( c_List_Olinorder__class_Osorted(c_List_Oremove1(X3,X1,X2),X2)
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1024,
[final] ).
cnf(c_0_1300,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1025,
[final] ).
cnf(c_0_1301,plain,
( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1026,
[final] ).
cnf(c_0_1302,plain,
( c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1027,
[final] ).
cnf(c_0_1303,plain,
( hBOOL(hAPP(X1,v_sko__List__XdropWhile__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
c_0_1028,
[final] ).
cnf(c_0_1304,plain,
( hBOOL(hAPP(X1,v_sko__List__Xtake__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
c_0_1029,
[final] ).
cnf(c_0_1305,plain,
( hBOOL(hAPP(X1,v_sko__List__Xconcat__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
c_0_1030,
[final] ).
cnf(c_0_1306,plain,
( hBOOL(hAPP(X1,v_sko__List__Xdistinct__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
c_0_1031,
[final] ).
cnf(c_0_1307,plain,
( hBOOL(hAPP(X1,v_sko__List__Xremove1__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
c_0_1032,
[final] ).
cnf(c_0_1308,plain,
( hBOOL(hAPP(X1,v_sko__List__Xlist__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
c_0_1033,
[final] ).
cnf(c_0_1309,plain,
( hBOOL(hAPP(X1,v_sko__List__Xmap__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
c_0_1034,
[final] ).
cnf(c_0_1310,plain,
( hAPP(hAPP(X2,X4),X1) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
c_0_1035,
[final] ).
cnf(c_0_1311,plain,
( hAPP(hAPP(X2,X1),X4) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
c_0_1036,
[final] ).
cnf(c_0_1312,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1037,
[final] ).
cnf(c_0_1313,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
c_0_1038,
[final] ).
cnf(c_0_1314,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
c_0_1039,
[final] ).
cnf(c_0_1315,plain,
( c_List_Oremdups(X1,X2) = X1
| c_Nat_Osize__class_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) != c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) ),
c_0_1040,
[final] ).
cnf(c_0_1316,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_1041,
[final] ).
cnf(c_0_1317,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
c_0_1042,
[final] ).
cnf(c_0_1318,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1043,
[final] ).
cnf(c_0_1319,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1044,
[final] ).
cnf(c_0_1320,plain,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
c_0_1045,
[final] ).
cnf(c_0_1321,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
c_0_1046,
[final] ).
cnf(c_0_1322,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
c_0_1047,
[final] ).
cnf(c_0_1323,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
c_0_1048,
[final] ).
cnf(c_0_1324,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
c_0_1049,
[final] ).
cnf(c_0_1325,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_1050,
[final] ).
cnf(c_0_1326,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1051,
[final] ).
cnf(c_0_1327,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1052,
[final] ).
cnf(c_0_1328,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1053,
[final] ).
cnf(c_0_1329,plain,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
c_0_1054,
[final] ).
cnf(c_0_1330,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1055,
[final] ).
cnf(c_0_1331,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_1056,
[final] ).
cnf(c_0_1332,plain,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_1057,
[final] ).
cnf(c_0_1333,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1058,
[final] ).
cnf(c_0_1334,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_1059,
[final] ).
cnf(c_0_1335,plain,
( X1 = c_List_Olist_ONil(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat) ),
c_0_1060,
[final] ).
cnf(c_0_1336,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Orotate(X3,X1,X2) != c_List_Olist_ONil(X2) ),
c_0_1061,
[final] ).
cnf(c_0_1337,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
c_0_1062,
[final] ).
cnf(c_0_1338,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
c_0_1063,
[final] ).
cnf(c_0_1339,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
c_0_1064,
[final] ).
cnf(c_0_1340,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
c_0_1065,
[final] ).
cnf(c_0_1341,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
c_0_1066,
[final] ).
cnf(c_0_1342,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X3,X2) != c_List_Olist_ONil(X2) ),
c_0_1067,
[final] ).
cnf(c_0_1343,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_1068,
[final] ).
cnf(c_0_1344,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1069,
[final] ).
cnf(c_0_1345,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_1070,
[final] ).
cnf(c_0_1346,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
c_0_1071,
[final] ).
cnf(c_0_1347,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
c_0_1072,
[final] ).
cnf(c_0_1348,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
c_0_1073,
[final] ).
cnf(c_0_1349,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
c_0_1074,
[final] ).
cnf(c_0_1350,plain,
( c_Nat_Osize__class_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2))
| c_List_Oremdups(X1,X2) != X1 ),
c_0_1075,
[final] ).
cnf(c_0_1351,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_1076,
[final] ).
cnf(c_0_1352,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_1077,
[final] ).
cnf(c_0_1353,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_1078,
[final] ).
cnf(c_0_1354,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1079,
[final] ).
cnf(c_0_1355,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1080,
[final] ).
cnf(c_0_1356,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1081,
[final] ).
cnf(c_0_1357,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1082,
[final] ).
cnf(c_0_1358,plain,
( c_List_Olinorder__class_Osorted(c_List_Oremdups(X1,X2),X2)
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_1083,
[final] ).
cnf(c_0_1359,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_1084,
[final] ).
cnf(c_0_1360,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_1085,
[final] ).
cnf(c_0_1361,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_1086,
[final] ).
cnf(c_0_1362,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
c_0_1087,
[final] ).
cnf(c_0_1363,plain,
( X1 = X2
| c_List_Orev(X1,X3) != c_List_Orev(X2,X3) ),
c_0_1088,
[final] ).
cnf(c_0_1364,plain,
( X1 = c_List_Olist_ONil(X2)
| c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) != c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_1089,
[final] ).
cnf(c_0_1365,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_1090,
[final] ).
cnf(c_0_1366,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_1091,
[final] ).
cnf(c_0_1367,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oremdups(X1,X2) != c_List_Olist_ONil(X2) ),
c_0_1092,
[final] ).
cnf(c_0_1368,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Orev(X1,X2) != c_List_Olist_ONil(X2) ),
c_0_1093,
[final] ).
cnf(c_0_1369,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oremdups(X1,X2) != c_List_Olist_ONil(X2) ),
c_0_1094,
[final] ).
cnf(c_0_1370,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Orev(X1,X2) != c_List_Olist_ONil(X2) ),
c_0_1095,
[final] ).
cnf(c_0_1371,plain,
( c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
c_0_1096,
[final] ).
cnf(c_0_1372,plain,
( c_List_Olinorder__class_Osorted(c_List_Olist_ONil(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_1097,
[final] ).
cnf(c_0_1373,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
c_0_1098,
[final] ).
cnf(c_0_1374,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
c_0_1099,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1100_0,axiom,
( c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1100]) ).
cnf(c_0_1100_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1100]) ).
cnf(c_0_1100_2,axiom,
( ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1100]) ).
cnf(c_0_1100_3,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4),X5,tc_Type_Otype,tc_Type_Otype) = X7 ),
inference(literals_permutation,[status(thm)],[c_0_1100]) ).
cnf(c_0_1101_0,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB) = X3
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1101]) ).
cnf(c_0_1101_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB,tc_Lambda_OdB) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1101]) ).
cnf(c_0_1102_0,axiom,
( c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1102]) ).
cnf(c_0_1102_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1102]) ).
cnf(c_0_1102_2,axiom,
( ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7) ),
inference(literals_permutation,[status(thm)],[c_0_1102]) ).
cnf(c_0_1102_3,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X7)
| ~ c_Type_Otypings(X1,X3,X6)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| c_Type_Otypings(X1,X4,c_Type_Osko__Type__Xvar__app__types__1__1(X5,X7,X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1102]) ).
cnf(c_0_1103_0,axiom,
( c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1103]) ).
cnf(c_0_1103_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3))
| c_ListOrder_Ostep1(c_Lambda_Obeta,X2,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X1,X2,X3),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1103]) ).
cnf(c_0_1104_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1104]) ).
cnf(c_0_1104_1,axiom,
( ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1104]) ).
cnf(c_0_1104_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1104]) ).
cnf(c_0_1105_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1105]) ).
cnf(c_0_1105_1,axiom,
( ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1105]) ).
cnf(c_0_1105_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1105]) ).
cnf(c_0_1106_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1106]) ).
cnf(c_0_1106_1,axiom,
( ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB)
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1106]) ).
cnf(c_0_1107_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1107]) ).
cnf(c_0_1107_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1107]) ).
cnf(c_0_1108_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1108]) ).
cnf(c_0_1108_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1108]) ).
cnf(c_0_1109_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1109]) ).
cnf(c_0_1109_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1109]) ).
cnf(c_0_1109_2,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X2))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1109]) ).
cnf(c_0_1110_0,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_List_Olist_Olist__case(X5,X2,c_List_Olist_OCons(X3,X4,t_b),t_a,t_b))) ),
inference(literals_permutation,[status(thm)],[c_0_1110]) ).
cnf(c_0_1110_1,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_Olist__case(X5,X2,c_List_Olist_OCons(X3,X4,t_b),t_a,t_b)))
| hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1110]) ).
cnf(c_0_1111_0,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_List_Olist_Olist__case(X5,X2,c_List_Olist_OCons(X3,X4,t_b),t_a,t_b))) ),
inference(literals_permutation,[status(thm)],[c_0_1111]) ).
cnf(c_0_1111_1,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_Olist__case(X5,X2,c_List_Olist_OCons(X3,X4,t_b),t_a,t_b)))
| hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1111]) ).
cnf(c_0_1112_0,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1112]) ).
cnf(c_0_1112_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a)))
| hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1112]) ).
cnf(c_0_1113_0,axiom,
( hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1113]) ).
cnf(c_0_1113_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X5,X2,X6,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4),t_a)))
| hBOOL(hAPP(X1,hAPP(hAPP(X2,X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1113]) ).
cnf(c_0_1114_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1114]) ).
cnf(c_0_1114_1,axiom,
( hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1114]) ).
cnf(c_0_1114_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X1)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__Xlem__1__3(X1)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1114]) ).
cnf(c_0_1115_0,axiom,
( hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1115]) ).
cnf(c_0_1115_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1)))
| ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1115]) ).
cnf(c_0_1115_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X1)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1115]) ).
cnf(c_0_1116_0,axiom,
( X4 = X5
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1116]) ).
cnf(c_0_1116_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| X4 = X5
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1116]) ).
cnf(c_0_1116_2,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| X4 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_1116]) ).
cnf(c_0_1117_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1117]) ).
cnf(c_0_1117_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1117]) ).
cnf(c_0_1118_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1118]) ).
cnf(c_0_1118_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X4,X5,X2,c_Lambda_OdB_OAbs(X3),t_a)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1118]) ).
cnf(c_0_1119_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1119]) ).
cnf(c_0_1119_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1119]) ).
cnf(c_0_1120_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1120]) ).
cnf(c_0_1120_1,axiom,
( ~ hBOOL(hAPP(X1,c_Lambda_OdB_OdB__case(X2,X4,X5,c_Lambda_OdB_OVar(X3),t_a)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1120]) ).
cnf(c_0_1121_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_Olist__case(X2,X3,c_List_Olist_ONil(t_b),t_a,t_b))) ),
inference(literals_permutation,[status(thm)],[c_0_1121]) ).
cnf(c_0_1121_1,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_Olist__case(X2,X3,c_List_Olist_ONil(t_b),t_a,t_b)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1121]) ).
cnf(c_0_1122_0,axiom,
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1122]) ).
cnf(c_0_1122_1,axiom,
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1122]) ).
cnf(c_0_1122_2,axiom,
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB)
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1122]) ).
cnf(c_0_1123_0,axiom,
( c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1123]) ).
cnf(c_0_1123_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)) ),
inference(literals_permutation,[status(thm)],[c_0_1123]) ).
cnf(c_0_1124_0,axiom,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1124]) ).
cnf(c_0_1124_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)) ),
inference(literals_permutation,[status(thm)],[c_0_1124]) ).
cnf(c_0_1125_0,axiom,
( c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1125]) ).
cnf(c_0_1125_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype)) ),
inference(literals_permutation,[status(thm)],[c_0_1125]) ).
cnf(c_0_1126_0,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1126]) ).
cnf(c_0_1126_1,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1126]) ).
cnf(c_0_1126_2,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1126]) ).
cnf(c_0_1126_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1126]) ).
cnf(c_0_1127_0,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1127]) ).
cnf(c_0_1127_1,axiom,
( c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1127]) ).
cnf(c_0_1127_2,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1127]) ).
cnf(c_0_1127_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1127]) ).
cnf(c_0_1128_0,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)
| c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1128]) ).
cnf(c_0_1128_1,axiom,
( c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1128]) ).
cnf(c_0_1129_0,axiom,
( c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(X1,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1129]) ).
cnf(c_0_1129_1,axiom,
( ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype))
| c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| ~ c_Type_Otypings(X1,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1129]) ).
cnf(c_0_1129_2,axiom,
( ~ c_Type_Otypings(X1,X5,X3)
| ~ c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X3,X4,tc_Type_Otype,tc_Type_Otype))
| c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X5,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1129]) ).
cnf(c_0_1130_0,axiom,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1130]) ).
cnf(c_0_1130_1,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1130]) ).
cnf(c_0_1130_2,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1130]) ).
cnf(c_0_1130_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1130]) ).
cnf(c_0_1131_0,axiom,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1131]) ).
cnf(c_0_1131_1,axiom,
( c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1131]) ).
cnf(c_0_1131_2,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1131]) ).
cnf(c_0_1131_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_sko__InductTermi__XIT__Xcases__4(X1),v_sko__InductTermi__XIT__Xcases__5(X1),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB)))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1131]) ).
cnf(c_0_1132_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1132]) ).
cnf(c_0_1132_1,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(literals_permutation,[status(thm)],[c_0_1132]) ).
cnf(c_0_1133_0,axiom,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1133]) ).
cnf(c_0_1133_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1133]) ).
cnf(c_0_1134_0,axiom,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1134]) ).
cnf(c_0_1134_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1134]) ).
cnf(c_0_1135_0,axiom,
( c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1135]) ).
cnf(c_0_1135_1,axiom,
( ~ c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
| c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1135]) ).
cnf(c_0_1136_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1136]) ).
cnf(c_0_1136_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1136]) ).
cnf(c_0_1137_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1137]) ).
cnf(c_0_1137_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1137]) ).
cnf(c_0_1138_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1138]) ).
cnf(c_0_1138_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1138]) ).
cnf(c_0_1139_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1139]) ).
cnf(c_0_1139_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1139]) ).
cnf(c_0_1140_0,axiom,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1))
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1140]) ).
cnf(c_0_1140_1,axiom,
( ~ class_OrderedGroup_Osemigroup__add(X1)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X4,X1,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X4,X1,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1140]) ).
cnf(c_0_1141_0,axiom,
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1141]) ).
cnf(c_0_1141_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1141]) ).
cnf(c_0_1142_0,axiom,
( c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1142]) ).
cnf(c_0_1142_1,axiom,
( ~ c_OrderedGroup_Osemigroup__add(X1,X2)
| c_List_Ofoldl(X1,hAPP(hAPP(X1,X3),X4),X5,X2,X2) = hAPP(hAPP(X1,X3),c_List_Ofoldl(X1,X4,X5,X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1142]) ).
cnf(c_0_1143_0,axiom,
( hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3)
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1143]) ).
cnf(c_0_1143_1,axiom,
( ~ c_OrderedGroup_Omonoid__add(X1,X2,X3)
| hAPP(hAPP(X2,X4),c_List_Ofoldl(X2,X1,X5,X3,X3)) = c_List_Ofoldl(X2,X4,X5,X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1143]) ).
cnf(c_0_1144_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1144]) ).
cnf(c_0_1144_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X3,c_HOL_Ozero__class_Ozero(X1),X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1144]) ).
cnf(c_0_1145_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1145]) ).
cnf(c_0_1145_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X3,X1,X1)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1145]) ).
cnf(c_0_1146_0,axiom,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1146]) ).
cnf(c_0_1146_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
| X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1146]) ).
cnf(c_0_1146_2,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X4,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X2
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1146]) ).
cnf(c_0_1147_0,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Oappend(X3,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_1147]) ).
cnf(c_0_1147_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB) != X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Oappend(X3,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1147]) ).
cnf(c_0_1148_0,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1148]) ).
cnf(c_0_1148_1,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1148]) ).
cnf(c_0_1148_2,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1148]) ).
cnf(c_0_1148_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1148]) ).
cnf(c_0_1149_0,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1149]) ).
cnf(c_0_1149_1,axiom,
( c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1149]) ).
cnf(c_0_1149_2,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1149]) ).
cnf(c_0_1149_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1149]) ).
cnf(c_0_1150_0,axiom,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Oappend(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X3,X4,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = X1
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3) != c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1150]) ).
cnf(c_0_1150_1,axiom,
( c_List_Oappend(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X3,X4,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = X1
| X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3) != c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1150]) ).
cnf(c_0_1150_2,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3) != c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| c_List_Oappend(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X2,X3,X4,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = X1
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1150]) ).
cnf(c_0_1151_0,axiom,
( c_Map_Omap__upds(X1,c_List_Oappend(X2,X3,X4),X5,X4,X6) = c_Map_Omap__upds(X1,X2,X5,X4,X6)
| c_Nat_Osize__class_Osize(X2,tc_List_Olist(X4)) != c_Nat_Osize__class_Osize(X5,tc_List_Olist(X6)) ),
inference(literals_permutation,[status(thm)],[c_0_1151]) ).
cnf(c_0_1151_1,axiom,
( c_Nat_Osize__class_Osize(X2,tc_List_Olist(X4)) != c_Nat_Osize__class_Osize(X5,tc_List_Olist(X6))
| c_Map_Omap__upds(X1,c_List_Oappend(X2,X3,X4),X5,X4,X6) = c_Map_Omap__upds(X1,X2,X5,X4,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1151]) ).
cnf(c_0_1152_0,axiom,
( c_Map_Omap__upds(X1,X2,c_List_Oappend(X3,X4,X5),X6,X5) = c_Map_Omap__upds(X1,X2,X3,X6,X5)
| c_Nat_Osize__class_Osize(X2,tc_List_Olist(X6)) != c_Nat_Osize__class_Osize(X3,tc_List_Olist(X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1152]) ).
cnf(c_0_1152_1,axiom,
( c_Nat_Osize__class_Osize(X2,tc_List_Olist(X6)) != c_Nat_Osize__class_Osize(X3,tc_List_Olist(X5))
| c_Map_Omap__upds(X1,X2,c_List_Oappend(X3,X4,X5),X6,X5) = c_Map_Omap__upds(X1,X2,X3,X6,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1152]) ).
cnf(c_0_1153_0,axiom,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1)
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1153]) ).
cnf(c_0_1153_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1),X2,X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1153]) ).
cnf(c_0_1154_0,axiom,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1154]) ).
cnf(c_0_1154_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(X1)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X1),X3,X2,X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1154]) ).
cnf(c_0_1155_0,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1155]) ).
cnf(c_0_1155_1,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1155]) ).
cnf(c_0_1156_0,axiom,
( X1 = c_Lambda_OdB_OAbs(X2)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1156]) ).
cnf(c_0_1156_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X2)
| X1 = c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1156]) ).
cnf(c_0_1157_0,axiom,
( c_Lambda_OdB_OAbs(X1) = X2
| c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1157]) ).
cnf(c_0_1157_1,axiom,
( c_Lambda_OdB_OAbs(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1157]) ).
cnf(c_0_1158_0,axiom,
( c_Lambda_OdB_OVar(X1) = X2
| c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1158]) ).
cnf(c_0_1158_1,axiom,
( c_Lambda_OdB_OVar(X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1158]) ).
cnf(c_0_1159_0,axiom,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1159]) ).
cnf(c_0_1159_1,axiom,
( c_Lambda_OdB_OAbs(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1159]) ).
cnf(c_0_1160_0,axiom,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1160]) ).
cnf(c_0_1160_1,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3)
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1160]) ).
cnf(c_0_1161_0,axiom,
( X1 = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1161]) ).
cnf(c_0_1161_1,axiom,
( c_Lambda_OdB_OVar(X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)
| X1 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1161]) ).
cnf(c_0_1162_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1162]) ).
cnf(c_0_1162_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X3),X4))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1162]) ).
cnf(c_0_1163_0,axiom,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1163]) ).
cnf(c_0_1163_1,axiom,
( hBOOL(hAPP(hAPP(X1,X3),X6))
| c_ListOrder_Ostep1(X1,X2,X5,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1163]) ).
cnf(c_0_1163_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| c_ListOrder_Ostep1(X1,X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1163]) ).
cnf(c_0_1164_0,axiom,
( c_ListOrder_Ostep1(X1,X2,X5,X4)
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1164]) ).
cnf(c_0_1164_1,axiom,
( X2 = X5
| c_ListOrder_Ostep1(X1,X2,X5,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1164]) ).
cnf(c_0_1164_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
| X2 = X5
| c_ListOrder_Ostep1(X1,X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1164]) ).
cnf(c_0_1165_0,axiom,
( X3 = X6
| hBOOL(hAPP(hAPP(X1,X3),X6))
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1165]) ).
cnf(c_0_1165_1,axiom,
( hBOOL(hAPP(hAPP(X1,X3),X6))
| X3 = X6
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1165]) ).
cnf(c_0_1165_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
| hBOOL(hAPP(hAPP(X1,X3),X6))
| X3 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_1165]) ).
cnf(c_0_1166_0,axiom,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1166]) ).
cnf(c_0_1166_1,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1166]) ).
cnf(c_0_1166_2,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1166]) ).
cnf(c_0_1166_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1166]) ).
cnf(c_0_1167_0,axiom,
( X1 = X2
| c_List_Olist__update(c_List_Olist__update(X3,X1,X4,X5),X2,X6,X5) = c_List_Olist__update(c_List_Olist__update(X3,X2,X6,X5),X1,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1167]) ).
cnf(c_0_1167_1,axiom,
( c_List_Olist__update(c_List_Olist__update(X3,X1,X4,X5),X2,X6,X5) = c_List_Olist__update(c_List_Olist__update(X3,X2,X6,X5),X1,X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1167]) ).
cnf(c_0_1168_0,axiom,
( X3 = X6
| X2 = X5
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1168]) ).
cnf(c_0_1168_1,axiom,
( X2 = X5
| X3 = X6
| ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1168]) ).
cnf(c_0_1168_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4),c_List_Oappend(X5,c_List_Olist_OCons(X6,c_List_Olist_ONil(X4),X4),X4),X4)
| X2 = X5
| X3 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_1168]) ).
cnf(c_0_1169_0,axiom,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1169]) ).
cnf(c_0_1169_1,axiom,
( c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1169]) ).
cnf(c_0_1169_2,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1169]) ).
cnf(c_0_1169_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X1))),v_sko__InductTermi__XIT__Xcases__5(X1)),v_sko__InductTermi__XIT__Xcases__6(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1169]) ).
cnf(c_0_1170_0,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1170]) ).
cnf(c_0_1170_1,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1170]) ).
cnf(c_0_1170_2,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1170]) ).
cnf(c_0_1170_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1170]) ).
cnf(c_0_1171_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1171]) ).
cnf(c_0_1171_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X1,X2,X2),X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1171]) ).
cnf(c_0_1172_0,axiom,
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1172]) ).
cnf(c_0_1172_1,axiom,
( c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1172]) ).
cnf(c_0_1172_2,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1172]) ).
cnf(c_0_1172_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X1)),v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1172]) ).
cnf(c_0_1173_0,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xtypes__snocE__1__1(X4,X1,X3,X2))
| ~ c_Type_Otypings(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1173]) ).
cnf(c_0_1173_1,axiom,
( ~ c_Type_Otypings(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X4)
| c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xtypes__snocE__1__1(X4,X1,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1173]) ).
cnf(c_0_1174_0,axiom,
( c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtypes__snocE__1__2(X4,X1,X3,X2))
| ~ c_Type_Otypings(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1174]) ).
cnf(c_0_1174_1,axiom,
( ~ c_Type_Otypings(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X4)
| c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtypes__snocE__1__2(X4,X1,X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1174]) ).
cnf(c_0_1175_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1175]) ).
cnf(c_0_1175_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1175]) ).
cnf(c_0_1175_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1175]) ).
cnf(c_0_1176_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1176]) ).
cnf(c_0_1176_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1176]) ).
cnf(c_0_1177_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1177]) ).
cnf(c_0_1177_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1177]) ).
cnf(c_0_1178_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1178]) ).
cnf(c_0_1178_1,axiom,
( c_ListOrder_Ostep1(X1,X3,X6,X4)
| hBOOL(hAPP(hAPP(X1,X2),X5))
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1178]) ).
cnf(c_0_1178_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| hBOOL(hAPP(hAPP(X1,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1178]) ).
cnf(c_0_1179_0,axiom,
( c_List_Olist__update(c_List_Oappend(X2,X4,X3),X1,X5,X3) = c_List_Oappend(c_List_Olist__update(X2,X1,X5,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1179]) ).
cnf(c_0_1179_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat)
| c_List_Olist__update(c_List_Oappend(X2,X4,X3),X1,X5,X3) = c_List_Oappend(c_List_Olist__update(X2,X1,X5,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1179]) ).
cnf(c_0_1180_0,axiom,
( c_List_Olist__update(c_List_Oappend(X2,X4,X3),X1,X5,X3) = c_List_Oappend(c_List_Olist__update(X2,X1,X5,X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1180]) ).
cnf(c_0_1180_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat)
| c_List_Olist__update(c_List_Oappend(X2,X4,X3),X1,X5,X3) = c_List_Oappend(c_List_Olist__update(X2,X1,X5,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1180]) ).
cnf(c_0_1181_0,axiom,
( c_List_Olistrelp(X1,c_List_Olist_OCons(X2,X4,X6),c_List_Olist_OCons(X3,X5,X6),X6)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_List_Olistrelp(X1,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1181]) ).
cnf(c_0_1181_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| c_List_Olistrelp(X1,c_List_Olist_OCons(X2,X4,X6),c_List_Olist_OCons(X3,X5,X6),X6)
| ~ c_List_Olistrelp(X1,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1181]) ).
cnf(c_0_1181_2,axiom,
( ~ c_List_Olistrelp(X1,X4,X5,X6)
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| c_List_Olistrelp(X1,c_List_Olist_OCons(X2,X4,X6),c_List_Olist_OCons(X3,X5,X6),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1181]) ).
cnf(c_0_1182_0,axiom,
( X6 = X3
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1182]) ).
cnf(c_0_1182_1,axiom,
( c_ListOrder_Ostep1(X1,X3,X6,X4)
| X6 = X3
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1182]) ).
cnf(c_0_1182_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
| c_ListOrder_Ostep1(X1,X3,X6,X4)
| X6 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1182]) ).
cnf(c_0_1183_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1183]) ).
cnf(c_0_1183_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X3,X1,X4)),c_Lambda_Osubst(X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1183]) ).
cnf(c_0_1184_0,axiom,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1184]) ).
cnf(c_0_1184_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1184]) ).
cnf(c_0_1185_0,axiom,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1185]) ).
cnf(c_0_1185_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1185]) ).
cnf(c_0_1186_0,axiom,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1186]) ).
cnf(c_0_1186_1,axiom,
( ~ c_ListOrder_Ostep1(X1,X2,X5,X4)
| c_ListOrder_Ostep1(X1,c_List_Oappend(X2,X3,X4),c_List_Oappend(X5,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1186]) ).
cnf(c_0_1187_0,axiom,
( c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1187]) ).
cnf(c_0_1187_1,axiom,
( ~ c_ListOrder_Ostep1(X1,X2,X3,X4)
| c_ListOrder_Ostep1(X1,c_List_Oappend(X5,X2,X4),c_List_Oappend(X5,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1187]) ).
cnf(c_0_1188_0,axiom,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ c_ListOrder_Ostep1(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1188]) ).
cnf(c_0_1188_1,axiom,
( ~ c_ListOrder_Ostep1(X1,X2,X3,X4)
| c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X5,X2,X4),c_List_Olist_OCons(X5,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1188]) ).
cnf(c_0_1189_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1189]) ).
cnf(c_0_1189_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1189]) ).
cnf(c_0_1190_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1190]) ).
cnf(c_0_1190_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1190]) ).
cnf(c_0_1191_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1191]) ).
cnf(c_0_1191_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X1,X3,X4)),c_Lambda_Osubst(X2,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_1191]) ).
cnf(c_0_1192_0,axiom,
( c_List_Ofilter(X2,c_List_Oappend(X5,c_List_Olist_OCons(X1,X3,X4),X4),X4) = c_List_Olist_OCons(X1,c_List_Ofilter(X2,X3,X4),X4)
| hBOOL(hAPP(X2,c_List_Osko__List__XCons__eq__filter__iff__1__3(X2,X5,X4)))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1192]) ).
cnf(c_0_1192_1,axiom,
( hBOOL(hAPP(X2,c_List_Osko__List__XCons__eq__filter__iff__1__3(X2,X5,X4)))
| c_List_Ofilter(X2,c_List_Oappend(X5,c_List_Olist_OCons(X1,X3,X4),X4),X4) = c_List_Olist_OCons(X1,c_List_Ofilter(X2,X3,X4),X4)
| ~ hBOOL(hAPP(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1192]) ).
cnf(c_0_1192_2,axiom,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(X2,c_List_Osko__List__XCons__eq__filter__iff__1__3(X2,X5,X4)))
| c_List_Ofilter(X2,c_List_Oappend(X5,c_List_Olist_OCons(X1,X3,X4),X4),X4) = c_List_Olist_OCons(X1,c_List_Ofilter(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1192]) ).
cnf(c_0_1193_0,axiom,
( c_List_Ofilter(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,X4,X5),X5),X5) = c_List_Olist_OCons(X3,c_List_Ofilter(X1,X4,X5),X5)
| hBOOL(hAPP(X1,c_List_Osko__List__Xfilter__eq__Cons__iff__1__3(X1,X2,X5)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1193]) ).
cnf(c_0_1193_1,axiom,
( hBOOL(hAPP(X1,c_List_Osko__List__Xfilter__eq__Cons__iff__1__3(X1,X2,X5)))
| c_List_Ofilter(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,X4,X5),X5),X5) = c_List_Olist_OCons(X3,c_List_Ofilter(X1,X4,X5),X5)
| ~ hBOOL(hAPP(X1,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1193]) ).
cnf(c_0_1193_2,axiom,
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X1,c_List_Osko__List__Xfilter__eq__Cons__iff__1__3(X1,X2,X5)))
| c_List_Ofilter(X1,c_List_Oappend(X2,c_List_Olist_OCons(X3,X4,X5),X5),X5) = c_List_Olist_OCons(X3,c_List_Ofilter(X1,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1193]) ).
cnf(c_0_1194_0,axiom,
( c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2))
| c_List_Omap(X4,X1,X2,X5) != c_List_Omap(X4,X3,X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1194]) ).
cnf(c_0_1194_1,axiom,
( c_List_Omap(X4,X1,X2,X5) != c_List_Omap(X4,X3,X2,X5)
| c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X3,tc_List_Olist(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1194]) ).
cnf(c_0_1195_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X5))
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1195]) ).
cnf(c_0_1195_1,axiom,
( X5 = X2
| hBOOL(hAPP(hAPP(X1,X2),X5))
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1195]) ).
cnf(c_0_1195_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
| X5 = X2
| hBOOL(hAPP(hAPP(X1,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1195]) ).
cnf(c_0_1196_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1196]) ).
cnf(c_0_1196_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1196]) ).
cnf(c_0_1196_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1196]) ).
cnf(c_0_1197_0,axiom,
( X6 = X3
| X5 = X2
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1197]) ).
cnf(c_0_1197_1,axiom,
( X5 = X2
| X6 = X3
| ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1197]) ).
cnf(c_0_1197_2,axiom,
( ~ c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X6,X4),X4)
| X5 = X2
| X6 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1197]) ).
cnf(c_0_1198_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1198]) ).
cnf(c_0_1198_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1198]) ).
cnf(c_0_1199_0,axiom,
( c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X2,X3,X4),X4)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,c_List_Olist_OCons(X2,X3,X4),X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1199]) ).
cnf(c_0_1199_1,axiom,
( ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,c_List_Olist_OCons(X2,X3,X4),X4),X4)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X2,X3,X4),X4)
| ~ class_Orderings_Olinorder(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1199]) ).
cnf(c_0_1199_2,axiom,
( ~ class_Orderings_Olinorder(X4)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,c_List_Olist_OCons(X2,X3,X4),X4),X4)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1199]) ).
cnf(c_0_1200_0,axiom,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1200]) ).
cnf(c_0_1200_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1200]) ).
cnf(c_0_1201_0,axiom,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1201]) ).
cnf(c_0_1201_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1201]) ).
cnf(c_0_1202_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1202]) ).
cnf(c_0_1202_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1202]) ).
cnf(c_0_1203_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1203]) ).
cnf(c_0_1203_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1203]) ).
cnf(c_0_1204_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1204]) ).
cnf(c_0_1204_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1204]) ).
cnf(c_0_1204_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X3),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1204]) ).
cnf(c_0_1205_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1205]) ).
cnf(c_0_1205_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1205]) ).
cnf(c_0_1205_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1205]) ).
cnf(c_0_1206_0,axiom,
( c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1206]) ).
cnf(c_0_1206_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X5))
| c_ListOrder_Ostep1(X1,c_List_Olist_OCons(X2,X3,X4),c_List_Olist_OCons(X5,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1206]) ).
cnf(c_0_1207_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1207]) ).
cnf(c_0_1207_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1207]) ).
cnf(c_0_1208_0,axiom,
( X1 = X2
| c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1208]) ).
cnf(c_0_1208_1,axiom,
( c_List_Oappend(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil(X4),X4),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1208]) ).
cnf(c_0_1209_0,axiom,
( X1 = X2
| c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1209]) ).
cnf(c_0_1209_1,axiom,
( c_List_Oappend(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil(X4),X4),X4) != c_List_Oappend(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil(X4),X4),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1209]) ).
cnf(c_0_1210_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xconcat__Xinduct__1(X1),v_sko__List__Xconcat__Xinduct__2(X1),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1210]) ).
cnf(c_0_1210_1,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xconcat__Xinduct__1(X1),v_sko__List__Xconcat__Xinduct__2(X1),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1210]) ).
cnf(c_0_1210_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xconcat__Xinduct__1(X1),v_sko__List__Xconcat__Xinduct__2(X1),t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1210]) ).
cnf(c_0_1211_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xtake__Xinduct__1(X1),v_sko__List__Xtake__Xinduct__2(X1),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1211]) ).
cnf(c_0_1211_1,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xtake__Xinduct__1(X1),v_sko__List__Xtake__Xinduct__2(X1),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1211]) ).
cnf(c_0_1211_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xtake__Xinduct__1(X1),v_sko__List__Xtake__Xinduct__2(X1),t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1211]) ).
cnf(c_0_1212_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xmap__Xinduct__1(X1),v_sko__List__Xmap__Xinduct__2(X1),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1212]) ).
cnf(c_0_1212_1,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xmap__Xinduct__1(X1),v_sko__List__Xmap__Xinduct__2(X1),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1212]) ).
cnf(c_0_1212_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xmap__Xinduct__1(X1),v_sko__List__Xmap__Xinduct__2(X1),t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1212]) ).
cnf(c_0_1213_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xlist__Xinduct__1(X1),v_sko__List__Xlist__Xinduct__2(X1),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1213]) ).
cnf(c_0_1213_1,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xlist__Xinduct__1(X1),v_sko__List__Xlist__Xinduct__2(X1),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1213]) ).
cnf(c_0_1213_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xlist__Xinduct__1(X1),v_sko__List__Xlist__Xinduct__2(X1),t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1213]) ).
cnf(c_0_1214_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__XdropWhile__Xinduct__1(X1),v_sko__List__XdropWhile__Xinduct__2(X1),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1214]) ).
cnf(c_0_1214_1,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__XdropWhile__Xinduct__1(X1),v_sko__List__XdropWhile__Xinduct__2(X1),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1214]) ).
cnf(c_0_1214_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__XdropWhile__Xinduct__1(X1),v_sko__List__XdropWhile__Xinduct__2(X1),t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1214]) ).
cnf(c_0_1215_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xremove1__Xinduct__1(X1),v_sko__List__Xremove1__Xinduct__2(X1),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1215]) ).
cnf(c_0_1215_1,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xremove1__Xinduct__1(X1),v_sko__List__Xremove1__Xinduct__2(X1),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1215]) ).
cnf(c_0_1215_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xremove1__Xinduct__1(X1),v_sko__List__Xremove1__Xinduct__2(X1),t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1215]) ).
cnf(c_0_1216_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xdistinct__Xinduct__1(X1),v_sko__List__Xdistinct__Xinduct__2(X1),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1216]) ).
cnf(c_0_1216_1,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xdistinct__Xinduct__1(X1),v_sko__List__Xdistinct__Xinduct__2(X1),t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1216]) ).
cnf(c_0_1216_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_OCons(v_sko__List__Xdistinct__Xinduct__1(X1),v_sko__List__Xdistinct__Xinduct__2(X1),t_a)))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1216]) ).
cnf(c_0_1217_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1217]) ).
cnf(c_0_1217_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1217]) ).
cnf(c_0_1218_0,axiom,
( c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1218]) ).
cnf(c_0_1218_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1218]) ).
cnf(c_0_1218_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1)
| c_HOL_Oord__class_Oless(X2,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1218]) ).
cnf(c_0_1219_0,axiom,
( c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1219]) ).
cnf(c_0_1219_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1219]) ).
cnf(c_0_1219_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1219]) ).
cnf(c_0_1220_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1220]) ).
cnf(c_0_1220_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1220]) ).
cnf(c_0_1221_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1221]) ).
cnf(c_0_1221_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1221]) ).
cnf(c_0_1221_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1221]) ).
cnf(c_0_1221_3,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X5),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1221]) ).
cnf(c_0_1222_0,axiom,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1222]) ).
cnf(c_0_1222_1,axiom,
( ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1222]) ).
cnf(c_0_1222_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X4),X2))
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1222]) ).
cnf(c_0_1223_0,axiom,
( c_Wellfounded_Oaccp(X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1223]) ).
cnf(c_0_1223_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| c_Wellfounded_Oaccp(X1,X3,X2)
| ~ c_Wellfounded_Oaccp(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1223]) ).
cnf(c_0_1223_2,axiom,
( ~ c_Wellfounded_Oaccp(X1,X4,X2)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| c_Wellfounded_Oaccp(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1223]) ).
cnf(c_0_1224_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1224]) ).
cnf(c_0_1224_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1224]) ).
cnf(c_0_1225_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1225]) ).
cnf(c_0_1225_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1225]) ).
cnf(c_0_1226_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1226]) ).
cnf(c_0_1226_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1226]) ).
cnf(c_0_1227_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1227]) ).
cnf(c_0_1227_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1227]) ).
cnf(c_0_1228_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1228]) ).
cnf(c_0_1228_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1228]) ).
cnf(c_0_1229_0,axiom,
( c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4)
| ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
| ~ c_Type_Otyping(X1,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1229]) ).
cnf(c_0_1229_1,axiom,
( ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
| c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4)
| ~ c_Type_Otyping(X1,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1229]) ).
cnf(c_0_1229_2,axiom,
( ~ c_Type_Otyping(X1,X5,X3)
| ~ c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))
| c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1229]) ).
cnf(c_0_1230_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1230]) ).
cnf(c_0_1230_1,axiom,
( c_List_Omap(X3,X1,X2,X4) != c_List_Olist_ONil(X4)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1230]) ).
cnf(c_0_1231_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1231]) ).
cnf(c_0_1231_1,axiom,
( c_List_Omap(X4,X1,X2,X3) != c_List_Olist_ONil(X3)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1231]) ).
cnf(c_0_1232_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Olist__update(X1,X3,X4,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1232]) ).
cnf(c_0_1232_1,axiom,
( c_List_Olist__update(X1,X3,X4,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1232]) ).
cnf(c_0_1233_0,axiom,
( c_Type_Otyping(X3,X2,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| ~ c_Type_Otyping(X3,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1233]) ).
cnf(c_0_1233_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| c_Type_Otyping(X3,X2,X4)
| ~ c_Type_Otyping(X3,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1233]) ).
cnf(c_0_1233_2,axiom,
( ~ c_Type_Otyping(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X2))
| c_Type_Otyping(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1233]) ).
cnf(c_0_1234_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1234]) ).
cnf(c_0_1234_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1234]) ).
cnf(c_0_1234_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1234]) ).
cnf(c_0_1235_0,axiom,
( c_List_Ofilter(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Ofilter(X1,X3,X4),X4)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1235]) ).
cnf(c_0_1235_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| c_List_Ofilter(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Ofilter(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1235]) ).
cnf(c_0_1236_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1236]) ).
cnf(c_0_1236_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1236]) ).
cnf(c_0_1236_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1236]) ).
cnf(c_0_1236_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1236]) ).
cnf(c_0_1237_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1237]) ).
cnf(c_0_1237_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1237]) ).
cnf(c_0_1237_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1237]) ).
cnf(c_0_1237_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1237]) ).
cnf(c_0_1238_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1238]) ).
cnf(c_0_1238_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1238]) ).
cnf(c_0_1238_2,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1238]) ).
cnf(c_0_1239_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1239]) ).
cnf(c_0_1239_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1239]) ).
cnf(c_0_1239_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1239]) ).
cnf(c_0_1240_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1240]) ).
cnf(c_0_1240_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1240]) ).
cnf(c_0_1240_2,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1240]) ).
cnf(c_0_1241_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1241]) ).
cnf(c_0_1241_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1241]) ).
cnf(c_0_1241_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1241]) ).
cnf(c_0_1242_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1242]) ).
cnf(c_0_1242_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X1,X3)),c_Lambda_Olift(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1242]) ).
cnf(c_0_1243_0,axiom,
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1243]) ).
cnf(c_0_1243_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1243]) ).
cnf(c_0_1243_2,axiom,
( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1243]) ).
cnf(c_0_1243_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1243]) ).
cnf(c_0_1244_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Osemigroup__add(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1244]) ).
cnf(c_0_1244_1,axiom,
( ~ c_OrderedGroup_Osemigroup__add(X1,X2)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1244]) ).
cnf(c_0_1245_0,axiom,
( c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| ~ c_List_Olistsp(X1,X2,X3)
| ~ c_List_Olistsp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1245]) ).
cnf(c_0_1245_1,axiom,
( ~ c_List_Olistsp(X1,X2,X3)
| c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| ~ c_List_Olistsp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1245]) ).
cnf(c_0_1245_2,axiom,
( ~ c_List_Olistsp(X1,X4,X3)
| ~ c_List_Olistsp(X1,X2,X3)
| c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1245]) ).
cnf(c_0_1246_0,axiom,
( X1 = X2
| c_List_Oremove1(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Oremove1(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1246]) ).
cnf(c_0_1246_1,axiom,
( c_List_Oremove1(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Olist_OCons(X2,c_List_Oremove1(X1,X3,X4),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1246]) ).
cnf(c_0_1247_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1247]) ).
cnf(c_0_1247_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1247]) ).
cnf(c_0_1247_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1247]) ).
cnf(c_0_1248_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1248]) ).
cnf(c_0_1248_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1248]) ).
cnf(c_0_1248_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1248]) ).
cnf(c_0_1249_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1249]) ).
cnf(c_0_1249_1,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1249]) ).
cnf(c_0_1249_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1249]) ).
cnf(c_0_1250_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1250]) ).
cnf(c_0_1250_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1250]) ).
cnf(c_0_1251_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1251]) ).
cnf(c_0_1251_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1251]) ).
cnf(c_0_1252_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1252]) ).
cnf(c_0_1252_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1252]) ).
cnf(c_0_1253_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1253]) ).
cnf(c_0_1253_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1253]) ).
cnf(c_0_1254_0,axiom,
( c_List_Olistsp(X1,X2,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1254]) ).
cnf(c_0_1254_1,axiom,
( ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4)
| c_List_Olistsp(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1254]) ).
cnf(c_0_1255_0,axiom,
( c_List_Olistsp(X1,X3,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1255]) ).
cnf(c_0_1255_1,axiom,
( ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4)
| c_List_Olistsp(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1255]) ).
cnf(c_0_1256_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1256]) ).
cnf(c_0_1256_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1256]) ).
cnf(c_0_1257_0,axiom,
( X1 = c_List_Oappend(c_List_Orev(X2,X3),c_List_Olist_OCons(X4,c_List_Olist_ONil(X3),X3),X3)
| c_List_Orev(X1,X3) != c_List_Olist_OCons(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1257]) ).
cnf(c_0_1257_1,axiom,
( c_List_Orev(X1,X3) != c_List_Olist_OCons(X4,X2,X3)
| X1 = c_List_Oappend(c_List_Orev(X2,X3),c_List_Olist_OCons(X4,c_List_Olist_ONil(X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1257]) ).
cnf(c_0_1258_0,axiom,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1258]) ).
cnf(c_0_1258_1,axiom,
( ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1258]) ).
cnf(c_0_1258_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X2))
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1258]) ).
cnf(c_0_1259_0,axiom,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1259]) ).
cnf(c_0_1259_1,axiom,
( ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1259]) ).
cnf(c_0_1259_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X2))
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| c_Wellfounded_Oaccp(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1259]) ).
cnf(c_0_1260_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1260]) ).
cnf(c_0_1260_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1260]) ).
cnf(c_0_1260_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1260]) ).
cnf(c_0_1261_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1261]) ).
cnf(c_0_1261_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1261]) ).
cnf(c_0_1261_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1261]) ).
cnf(c_0_1262_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1262]) ).
cnf(c_0_1262_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1262]) ).
cnf(c_0_1262_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1262]) ).
cnf(c_0_1263_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1263]) ).
cnf(c_0_1263_1,axiom,
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1263]) ).
cnf(c_0_1264_0,axiom,
( c_List_Ofilter(X1,c_List_Oreplicate(X3,X2,X4),X4) = c_List_Oreplicate(X3,X2,X4)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1264]) ).
cnf(c_0_1264_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| c_List_Ofilter(X1,c_List_Oreplicate(X3,X2,X4),X4) = c_List_Oreplicate(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1264]) ).
cnf(c_0_1265_0,axiom,
( c_Type_Otyping(X1,X4,X3)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1265]) ).
cnf(c_0_1265_1,axiom,
( ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otyping(X1,X4,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1265]) ).
cnf(c_0_1265_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4))
| ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otyping(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1265]) ).
cnf(c_0_1266_0,axiom,
( hBOOL(hAPP(X1,X2))
| c_List_Oremove1(X2,c_List_Ofilter(X1,X3,X4),X4) = c_List_Ofilter(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1266]) ).
cnf(c_0_1266_1,axiom,
( c_List_Oremove1(X2,c_List_Ofilter(X1,X3,X4),X4) = c_List_Ofilter(X1,X3,X4)
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1266]) ).
cnf(c_0_1267_0,axiom,
( hBOOL(hAPP(X1,X2))
| c_List_Ofilter(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Ofilter(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1267]) ).
cnf(c_0_1267_1,axiom,
( c_List_Ofilter(X1,c_List_Olist_OCons(X2,X3,X4),X4) = c_List_Ofilter(X1,X3,X4)
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1267]) ).
cnf(c_0_1268_0,axiom,
( c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1268]) ).
cnf(c_0_1268_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1268]) ).
cnf(c_0_1268_2,axiom,
( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1268]) ).
cnf(c_0_1268_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1268]) ).
cnf(c_0_1269_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1269]) ).
cnf(c_0_1269_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1269]) ).
cnf(c_0_1269_2,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1269]) ).
cnf(c_0_1269_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X4,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1269]) ).
cnf(c_0_1270_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1270]) ).
cnf(c_0_1270_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1270]) ).
cnf(c_0_1271_0,axiom,
( c_List_Olinorder__class_Osorted(X2,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1271]) ).
cnf(c_0_1271_1,axiom,
( ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,X2,X3),X3)
| c_List_Olinorder__class_Osorted(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1271]) ).
cnf(c_0_1271_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,X2,X3),X3)
| c_List_Olinorder__class_Osorted(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1271]) ).
cnf(c_0_1272_0,axiom,
( c_List_Olinorder__class_Osorted(X1,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X1,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1272]) ).
cnf(c_0_1272_1,axiom,
( ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X1,X2,X3),X3)
| c_List_Olinorder__class_Osorted(X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1272]) ).
cnf(c_0_1272_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X1,X2,X3),X3)
| c_List_Olinorder__class_Osorted(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1272]) ).
cnf(c_0_1273_0,axiom,
( c_List_Olinorder__class_Osorted(X2,X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X1,X2,X3),X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1273]) ).
cnf(c_0_1273_1,axiom,
( ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X1,X2,X3),X3)
| c_List_Olinorder__class_Osorted(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1273]) ).
cnf(c_0_1273_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X1,X2,X3),X3)
| c_List_Olinorder__class_Osorted(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1273]) ).
cnf(c_0_1274_0,axiom,
( hBOOL(hAPP(X1,X2))
| c_List_Olist_OCons(X2,X3,X4) != c_List_Ofilter(X1,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1274]) ).
cnf(c_0_1274_1,axiom,
( c_List_Olist_OCons(X2,X3,X4) != c_List_Ofilter(X1,X5,X4)
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1274]) ).
cnf(c_0_1275_0,axiom,
( hBOOL(hAPP(X1,X2))
| c_List_Ofilter(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1275]) ).
cnf(c_0_1275_1,axiom,
( c_List_Ofilter(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4)
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1275]) ).
cnf(c_0_1276_0,axiom,
( hBOOL(hAPP(X1,X2))
| c_List_Ofilter(X1,c_List_Oreplicate(X3,X2,X4),X4) = c_List_Olist_ONil(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1276]) ).
cnf(c_0_1276_1,axiom,
( c_List_Ofilter(X1,c_List_Oreplicate(X3,X2,X4),X4) = c_List_Olist_ONil(X4)
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1276]) ).
cnf(c_0_1277_0,axiom,
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1277]) ).
cnf(c_0_1277_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1277]) ).
cnf(c_0_1278_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1278]) ).
cnf(c_0_1278_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1278]) ).
cnf(c_0_1278_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1278]) ).
cnf(c_0_1278_3,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X1))
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1278]) ).
cnf(c_0_1279_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1279]) ).
cnf(c_0_1279_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1279]) ).
cnf(c_0_1279_2,axiom,
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1279]) ).
cnf(c_0_1279_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1279]) ).
cnf(c_0_1280_0,axiom,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1280]) ).
cnf(c_0_1280_1,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1280]) ).
cnf(c_0_1280_2,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1280]) ).
cnf(c_0_1280_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X1)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1280]) ).
cnf(c_0_1281_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1281]) ).
cnf(c_0_1281_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1281]) ).
cnf(c_0_1281_2,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1281]) ).
cnf(c_0_1282_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1282]) ).
cnf(c_0_1282_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1282]) ).
cnf(c_0_1282_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1282]) ).
cnf(c_0_1283_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1283]) ).
cnf(c_0_1283_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1283]) ).
cnf(c_0_1283_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1283]) ).
cnf(c_0_1284_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1284]) ).
cnf(c_0_1284_1,axiom,
( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1284]) ).
cnf(c_0_1284_2,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1284]) ).
cnf(c_0_1285_0,axiom,
( X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3)
| c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3) != c_List_Orev(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1285]) ).
cnf(c_0_1285_1,axiom,
( c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3) != c_List_Orev(X1,X3)
| X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1285]) ).
cnf(c_0_1286_0,axiom,
( X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3)
| c_List_Orev(X1,X3) != c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1286]) ).
cnf(c_0_1286_1,axiom,
( c_List_Orev(X1,X3) != c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3)
| X1 = c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1286]) ).
cnf(c_0_1287_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = X3
| c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1287]) ).
cnf(c_0_1287_1,axiom,
( X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1287]) ).
cnf(c_0_1287_2,axiom,
( c_List_Oreplicate(X1,X2,X4) != c_List_Oreplicate(X5,X3,X4)
| X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1287]) ).
cnf(c_0_1288_0,axiom,
( X1 = X2
| c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1288]) ).
cnf(c_0_1288_1,axiom,
( c_List_Oreplicate(X1,X3,X4) != c_List_Oreplicate(X2,X5,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1288]) ).
cnf(c_0_1289_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1289]) ).
cnf(c_0_1289_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1289]) ).
cnf(c_0_1289_2,axiom,
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1289]) ).
cnf(c_0_1290_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1290]) ).
cnf(c_0_1290_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1290]) ).
cnf(c_0_1290_2,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1290]) ).
cnf(c_0_1291_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1291]) ).
cnf(c_0_1291_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1291]) ).
cnf(c_0_1291_2,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1291]) ).
cnf(c_0_1292_0,axiom,
( X1 = X2
| c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1292]) ).
cnf(c_0_1292_1,axiom,
( c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1292]) ).
cnf(c_0_1293_0,axiom,
( X1 = X2
| c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1293]) ).
cnf(c_0_1293_1,axiom,
( c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1293]) ).
cnf(c_0_1294_0,axiom,
( X1 = X2
| c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1294]) ).
cnf(c_0_1294_1,axiom,
( c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1294]) ).
cnf(c_0_1295_0,axiom,
( X1 = X2
| c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1295]) ).
cnf(c_0_1295_1,axiom,
( c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1295]) ).
cnf(c_0_1296_0,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1296]) ).
cnf(c_0_1296_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(literals_permutation,[status(thm)],[c_0_1296]) ).
cnf(c_0_1297_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1297]) ).
cnf(c_0_1297_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1297]) ).
cnf(c_0_1298_0,axiom,
( c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1298]) ).
cnf(c_0_1298_1,axiom,
( c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1298]) ).
cnf(c_0_1298_2,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1298]) ).
cnf(c_0_1298_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X1)))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X1)) = X1
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X1),tc_Lambda_OdB) ),
inference(literals_permutation,[status(thm)],[c_0_1298]) ).
cnf(c_0_1299_0,axiom,
( c_List_Olinorder__class_Osorted(c_List_Oremove1(X3,X1,X2),X2)
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1299]) ).
cnf(c_0_1299_1,axiom,
( ~ c_List_Olinorder__class_Osorted(X1,X2)
| c_List_Olinorder__class_Osorted(c_List_Oremove1(X3,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1299]) ).
cnf(c_0_1299_2,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| c_List_Olinorder__class_Osorted(c_List_Oremove1(X3,X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1299]) ).
cnf(c_0_1300_0,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1300]) ).
cnf(c_0_1300_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1300]) ).
cnf(c_0_1301_0,axiom,
( c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1301]) ).
cnf(c_0_1301_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Oliftn(X3,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1301]) ).
cnf(c_0_1302_0,axiom,
( c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1302]) ).
cnf(c_0_1302_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1302]) ).
cnf(c_0_1303_0,axiom,
( hBOOL(hAPP(X1,v_sko__List__XdropWhile__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1303]) ).
cnf(c_0_1303_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__XdropWhile__Xinduct__2(X1)))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1303]) ).
cnf(c_0_1303_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__XdropWhile__Xinduct__2(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1303]) ).
cnf(c_0_1304_0,axiom,
( hBOOL(hAPP(X1,v_sko__List__Xtake__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1304]) ).
cnf(c_0_1304_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xtake__Xinduct__2(X1)))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1304]) ).
cnf(c_0_1304_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xtake__Xinduct__2(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1304]) ).
cnf(c_0_1305_0,axiom,
( hBOOL(hAPP(X1,v_sko__List__Xconcat__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1305]) ).
cnf(c_0_1305_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xconcat__Xinduct__2(X1)))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1305]) ).
cnf(c_0_1305_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xconcat__Xinduct__2(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1305]) ).
cnf(c_0_1306_0,axiom,
( hBOOL(hAPP(X1,v_sko__List__Xdistinct__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1306]) ).
cnf(c_0_1306_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xdistinct__Xinduct__2(X1)))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1306]) ).
cnf(c_0_1306_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xdistinct__Xinduct__2(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1306]) ).
cnf(c_0_1307_0,axiom,
( hBOOL(hAPP(X1,v_sko__List__Xremove1__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1307]) ).
cnf(c_0_1307_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xremove1__Xinduct__2(X1)))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1307]) ).
cnf(c_0_1307_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xremove1__Xinduct__2(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1307]) ).
cnf(c_0_1308_0,axiom,
( hBOOL(hAPP(X1,v_sko__List__Xlist__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1308]) ).
cnf(c_0_1308_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xlist__Xinduct__2(X1)))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1308]) ).
cnf(c_0_1308_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xlist__Xinduct__2(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1308]) ).
cnf(c_0_1309_0,axiom,
( hBOOL(hAPP(X1,v_sko__List__Xmap__Xinduct__2(X1)))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1309]) ).
cnf(c_0_1309_1,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xmap__Xinduct__2(X1)))
| ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a))) ),
inference(literals_permutation,[status(thm)],[c_0_1309]) ).
cnf(c_0_1309_2,axiom,
( ~ hBOOL(hAPP(X1,c_List_Olist_ONil(t_a)))
| hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,v_sko__List__Xmap__Xinduct__2(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1309]) ).
cnf(c_0_1310_0,axiom,
( hAPP(hAPP(X2,X4),X1) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1310]) ).
cnf(c_0_1310_1,axiom,
( ~ c_OrderedGroup_Omonoid__add(X1,X2,X3)
| hAPP(hAPP(X2,X4),X1) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1310]) ).
cnf(c_0_1311_0,axiom,
( hAPP(hAPP(X2,X1),X4) = X4
| ~ c_OrderedGroup_Omonoid__add(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1311]) ).
cnf(c_0_1311_1,axiom,
( ~ c_OrderedGroup_Omonoid__add(X1,X2,X3)
| hAPP(hAPP(X2,X1),X4) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1311]) ).
cnf(c_0_1312_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1312]) ).
cnf(c_0_1312_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_1312]) ).
cnf(c_0_1313_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1313]) ).
cnf(c_0_1313_1,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1313]) ).
cnf(c_0_1313_2,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2)
| X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1313]) ).
cnf(c_0_1314_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X2 = X1
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1314]) ).
cnf(c_0_1314_1,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1314]) ).
cnf(c_0_1314_2,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2)
| X2 = X1
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1314]) ).
cnf(c_0_1315_0,axiom,
( c_List_Oremdups(X1,X2) = X1
| c_Nat_Osize__class_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) != c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1315]) ).
cnf(c_0_1315_1,axiom,
( c_Nat_Osize__class_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) != c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2))
| c_List_Oremdups(X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1315]) ).
cnf(c_0_1316_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1316]) ).
cnf(c_0_1316_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1316]) ).
cnf(c_0_1316_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1316]) ).
cnf(c_0_1316_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1316]) ).
cnf(c_0_1317_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1317]) ).
cnf(c_0_1317_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1317]) ).
cnf(c_0_1317_2,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1317]) ).
cnf(c_0_1317_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1317]) ).
cnf(c_0_1318_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1318]) ).
cnf(c_0_1318_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1318]) ).
cnf(c_0_1318_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1318]) ).
cnf(c_0_1318_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1318]) ).
cnf(c_0_1319_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1319]) ).
cnf(c_0_1319_1,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1319]) ).
cnf(c_0_1319_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1319]) ).
cnf(c_0_1319_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1319]) ).
cnf(c_0_1320_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,X3)
| c_HOL_Oord__class_Oless(X2,X1,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1320]) ).
cnf(c_0_1320_1,axiom,
( c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1320]) ).
cnf(c_0_1320_2,axiom,
( X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1320]) ).
cnf(c_0_1320_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| X2 = X1
| c_HOL_Oord__class_Oless(X2,X1,X3)
| c_HOL_Oord__class_Oless(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1320]) ).
cnf(c_0_1321_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1321]) ).
cnf(c_0_1321_1,axiom,
( hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1321]) ).
cnf(c_0_1322_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1322]) ).
cnf(c_0_1322_1,axiom,
( hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1322]) ).
cnf(c_0_1323_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1323]) ).
cnf(c_0_1323_1,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1323]) ).
cnf(c_0_1324_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1324]) ).
cnf(c_0_1324_1,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1324]) ).
cnf(c_0_1325_0,axiom,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1325]) ).
cnf(c_0_1325_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1325]) ).
cnf(c_0_1326_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1326]) ).
cnf(c_0_1326_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1326]) ).
cnf(c_0_1327_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1327]) ).
cnf(c_0_1327_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1327]) ).
cnf(c_0_1328_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1328]) ).
cnf(c_0_1328_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1328]) ).
cnf(c_0_1329_0,axiom,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1329]) ).
cnf(c_0_1329_1,axiom,
( ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3)
| hAPP(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1329]) ).
cnf(c_0_1330_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1330]) ).
cnf(c_0_1330_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1330]) ).
cnf(c_0_1330_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1330]) ).
cnf(c_0_1331_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1331]) ).
cnf(c_0_1331_1,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1331]) ).
cnf(c_0_1331_2,axiom,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1331]) ).
cnf(c_0_1332_0,axiom,
( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1332]) ).
cnf(c_0_1332_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1332]) ).
cnf(c_0_1333_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1333]) ).
cnf(c_0_1333_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1333]) ).
cnf(c_0_1333_2,axiom,
( ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1333]) ).
cnf(c_0_1333_3,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1333]) ).
cnf(c_0_1334_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1334]) ).
cnf(c_0_1334_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1334]) ).
cnf(c_0_1334_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1334]) ).
cnf(c_0_1335_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1335]) ).
cnf(c_0_1335_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),tc_nat)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1335]) ).
cnf(c_0_1336_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Orotate(X3,X1,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1336]) ).
cnf(c_0_1336_1,axiom,
( c_List_Orotate(X3,X1,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1336]) ).
cnf(c_0_1337_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1337]) ).
cnf(c_0_1337_1,axiom,
( c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1337]) ).
cnf(c_0_1338_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1338]) ).
cnf(c_0_1338_1,axiom,
( c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1338]) ).
cnf(c_0_1339_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1339]) ).
cnf(c_0_1339_1,axiom,
( c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1339]) ).
cnf(c_0_1340_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1340]) ).
cnf(c_0_1340_1,axiom,
( c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1340]) ).
cnf(c_0_1341_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1341]) ).
cnf(c_0_1341_1,axiom,
( c_List_Oreplicate(X1,X2,X3) != c_List_Olist_ONil(X3)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1341]) ).
cnf(c_0_1342_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(X1,X3,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1342]) ).
cnf(c_0_1342_1,axiom,
( c_List_Oreplicate(X1,X3,X2) != c_List_Olist_ONil(X2)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1342]) ).
cnf(c_0_1343_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1343]) ).
cnf(c_0_1343_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1343]) ).
cnf(c_0_1344_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1344]) ).
cnf(c_0_1344_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1344]) ).
cnf(c_0_1345_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1345]) ).
cnf(c_0_1345_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1345]) ).
cnf(c_0_1346_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1346]) ).
cnf(c_0_1346_1,axiom,
( c_List_Oappend(X1,X3,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1346]) ).
cnf(c_0_1347_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1347]) ).
cnf(c_0_1347_1,axiom,
( c_List_Oappend(X1,X3,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1347]) ).
cnf(c_0_1348_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1348]) ).
cnf(c_0_1348_1,axiom,
( c_List_Oappend(X3,X1,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1348]) ).
cnf(c_0_1349_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_1349]) ).
cnf(c_0_1349_1,axiom,
( c_List_Oappend(X3,X1,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1349]) ).
cnf(c_0_1350_0,axiom,
( c_Nat_Osize__class_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2))
| c_List_Oremdups(X1,X2) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_1350]) ).
cnf(c_0_1350_1,axiom,
( c_List_Oremdups(X1,X2) != X1
| c_Nat_Osize__class_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1350]) ).
cnf(c_0_1351_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1351]) ).
cnf(c_0_1351_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_1351]) ).
cnf(c_0_1352_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1352]) ).
cnf(c_0_1352_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1352]) ).
cnf(c_0_1353_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1353]) ).
cnf(c_0_1353_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1353]) ).
cnf(c_0_1353_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1353]) ).
cnf(c_0_1354_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1354]) ).
cnf(c_0_1354_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1354]) ).
cnf(c_0_1355_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1355]) ).
cnf(c_0_1355_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1355]) ).
cnf(c_0_1356_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1356]) ).
cnf(c_0_1356_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1356]) ).
cnf(c_0_1357_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1357]) ).
cnf(c_0_1357_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1357]) ).
cnf(c_0_1358_0,axiom,
( c_List_Olinorder__class_Osorted(c_List_Oremdups(X1,X2),X2)
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1358]) ).
cnf(c_0_1358_1,axiom,
( ~ c_List_Olinorder__class_Osorted(X1,X2)
| c_List_Olinorder__class_Osorted(c_List_Oremdups(X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1358]) ).
cnf(c_0_1358_2,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_List_Olinorder__class_Osorted(X1,X2)
| c_List_Olinorder__class_Osorted(c_List_Oremdups(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1358]) ).
cnf(c_0_1359_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1359]) ).
cnf(c_0_1359_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1359]) ).
cnf(c_0_1360_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1360]) ).
cnf(c_0_1360_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1360]) ).
cnf(c_0_1361_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1361]) ).
cnf(c_0_1361_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1361]) ).
cnf(c_0_1362_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1362]) ).
cnf(c_0_1362_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1362]) ).
cnf(c_0_1363_0,axiom,
( X1 = X2
| c_List_Orev(X1,X3) != c_List_Orev(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1363]) ).
cnf(c_0_1363_1,axiom,
( c_List_Orev(X1,X3) != c_List_Orev(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1363]) ).
cnf(c_0_1364_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_1364]) ).
cnf(c_0_1364_1,axiom,
( c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1364]) ).
cnf(c_0_1365_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1365]) ).
cnf(c_0_1365_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1365]) ).
cnf(c_0_1366_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1366]) ).
cnf(c_0_1366_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1366]) ).
cnf(c_0_1367_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oremdups(X1,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1367]) ).
cnf(c_0_1367_1,axiom,
( c_List_Oremdups(X1,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1367]) ).
cnf(c_0_1368_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Orev(X1,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1368]) ).
cnf(c_0_1368_1,axiom,
( c_List_Orev(X1,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1368]) ).
cnf(c_0_1369_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oremdups(X1,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1369]) ).
cnf(c_0_1369_1,axiom,
( c_List_Oremdups(X1,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1369]) ).
cnf(c_0_1370_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Orev(X1,X2) != c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1370]) ).
cnf(c_0_1370_1,axiom,
( c_List_Orev(X1,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1370]) ).
cnf(c_0_1371_0,axiom,
( c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1)
| ~ class_OrderedGroup_Osemigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1371]) ).
cnf(c_0_1371_1,axiom,
( ~ class_OrderedGroup_Osemigroup__add(X1)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1371]) ).
cnf(c_0_1372_0,axiom,
( c_List_Olinorder__class_Osorted(c_List_Olist_ONil(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_1372]) ).
cnf(c_0_1372_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_List_Olinorder__class_Osorted(c_List_Olist_ONil(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_1372]) ).
cnf(c_0_1373_0,axiom,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1373]) ).
cnf(c_0_1373_1,axiom,
( c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1373]) ).
cnf(c_0_1374_0,axiom,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_1374]) ).
cnf(c_0_1374_1,axiom,
( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1374]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_726,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_1_727,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_2_728,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_1 ).
cnf(c_0_3_729,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_730,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_84,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,X0,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X0,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_909855.p',c_0_1132_0) ).
cnf(c_1238,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,X0,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X0,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(copy,[status(esa)],[c_84]) ).
cnf(c_20083,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(instantiation,[status(thm)],[c_1238]) ).
cnf(c_38525,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(instantiation,[status(thm)],[c_20083]) ).
cnf(c_730,plain,
c_List_Olistsp(X0,c_List_Olist_ONil(X1),X1),
file('/export/starexec/sandbox/tmp/iprover_modulo_909855.p',c_0_680_0) ).
cnf(c_1884,plain,
c_List_Olistsp(X0,c_List_Olist_ONil(X1),X1),
inference(copy,[status(esa)],[c_730]) ).
cnf(c_20082,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),
inference(instantiation,[status(thm)],[c_1884]) ).
cnf(c_831,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/tmp/iprover_modulo_909855.p',c_0_4) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_38525,c_20082,c_831]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL763-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : iprover_modulo %s %d
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 6 00:37:15 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Running in mono-core mode
% 0.16/0.48 % Orienting using strategy Equiv(ClausalAll)
% 0.16/0.48 % Orientation found
% 0.16/0.48 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_d73ac6.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_909855.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_2bfa66 | grep -v "SZS"
% 0.16/0.51
% 0.16/0.51 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.16/0.51
% 0.16/0.51 %
% 0.16/0.51 % ------ iProver source info
% 0.16/0.51
% 0.16/0.51 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.16/0.51 % git: non_committed_changes: true
% 0.16/0.51 % git: last_make_outside_of_git: true
% 0.16/0.51
% 0.16/0.51 %
% 0.16/0.51 % ------ Input Options
% 0.16/0.51
% 0.16/0.51 % --out_options all
% 0.16/0.51 % --tptp_safe_out true
% 0.16/0.51 % --problem_path ""
% 0.16/0.51 % --include_path ""
% 0.16/0.51 % --clausifier .//eprover
% 0.16/0.51 % --clausifier_options --tstp-format
% 0.16/0.51 % --stdin false
% 0.16/0.51 % --dbg_backtrace false
% 0.16/0.51 % --dbg_dump_prop_clauses false
% 0.16/0.51 % --dbg_dump_prop_clauses_file -
% 0.16/0.51 % --dbg_out_stat false
% 0.16/0.51
% 0.16/0.51 % ------ General Options
% 0.16/0.51
% 0.16/0.51 % --fof false
% 0.16/0.51 % --time_out_real 150.
% 0.16/0.51 % --time_out_prep_mult 0.2
% 0.16/0.51 % --time_out_virtual -1.
% 0.16/0.51 % --schedule none
% 0.16/0.51 % --ground_splitting input
% 0.16/0.51 % --splitting_nvd 16
% 0.16/0.51 % --non_eq_to_eq false
% 0.16/0.51 % --prep_gs_sim true
% 0.16/0.51 % --prep_unflatten false
% 0.16/0.51 % --prep_res_sim true
% 0.16/0.51 % --prep_upred true
% 0.16/0.51 % --res_sim_input true
% 0.16/0.51 % --clause_weak_htbl true
% 0.16/0.51 % --gc_record_bc_elim false
% 0.16/0.51 % --symbol_type_check false
% 0.16/0.51 % --clausify_out false
% 0.16/0.51 % --large_theory_mode false
% 0.16/0.51 % --prep_sem_filter none
% 0.16/0.51 % --prep_sem_filter_out false
% 0.16/0.51 % --preprocessed_out false
% 0.16/0.51 % --sub_typing false
% 0.16/0.51 % --brand_transform false
% 0.16/0.51 % --pure_diseq_elim true
% 0.16/0.51 % --min_unsat_core false
% 0.16/0.51 % --pred_elim true
% 0.16/0.51 % --add_important_lit false
% 0.16/0.51 % --soft_assumptions false
% 0.16/0.51 % --reset_solvers false
% 0.16/0.51 % --bc_imp_inh []
% 0.16/0.51 % --conj_cone_tolerance 1.5
% 0.16/0.51 % --prolific_symb_bound 500
% 0.16/0.51 % --lt_threshold 2000
% 0.16/0.51
% 0.16/0.51 % ------ SAT Options
% 0.16/0.51
% 0.16/0.51 % --sat_mode false
% 0.16/0.51 % --sat_fm_restart_options ""
% 0.16/0.51 % --sat_gr_def false
% 0.16/0.51 % --sat_epr_types true
% 0.16/0.51 % --sat_non_cyclic_types false
% 0.16/0.51 % --sat_finite_models false
% 0.16/0.51 % --sat_fm_lemmas false
% 0.16/0.51 % --sat_fm_prep false
% 0.16/0.51 % --sat_fm_uc_incr true
% 0.16/0.51 % --sat_out_model small
% 0.16/0.51 % --sat_out_clauses false
% 0.16/0.51
% 0.16/0.51 % ------ QBF Options
% 0.16/0.51
% 0.16/0.51 % --qbf_mode false
% 0.16/0.51 % --qbf_elim_univ true
% 0.16/0.51 % --qbf_sk_in true
% 0.16/0.51 % --qbf_pred_elim true
% 0.16/0.51 % --qbf_split 32
% 0.16/0.51
% 0.16/0.51 % ------ BMC1 Options
% 0.16/0.51
% 0.16/0.51 % --bmc1_incremental false
% 0.16/0.51 % --bmc1_axioms reachable_all
% 0.16/0.51 % --bmc1_min_bound 0
% 0.16/0.51 % --bmc1_max_bound -1
% 0.16/0.51 % --bmc1_max_bound_default -1
% 0.16/0.51 % --bmc1_symbol_reachability true
% 0.16/0.51 % --bmc1_property_lemmas false
% 0.16/0.51 % --bmc1_k_induction false
% 0.16/0.51 % --bmc1_non_equiv_states false
% 0.16/0.51 % --bmc1_deadlock false
% 0.16/0.51 % --bmc1_ucm false
% 0.16/0.51 % --bmc1_add_unsat_core none
% 0.16/0.51 % --bmc1_unsat_core_children false
% 0.16/0.51 % --bmc1_unsat_core_extrapolate_axioms false
% 0.16/0.51 % --bmc1_out_stat full
% 0.16/0.51 % --bmc1_ground_init false
% 0.16/0.51 % --bmc1_pre_inst_next_state false
% 0.16/0.51 % --bmc1_pre_inst_state false
% 0.16/0.51 % --bmc1_pre_inst_reach_state false
% 0.16/0.51 % --bmc1_out_unsat_core false
% 0.16/0.51 % --bmc1_aig_witness_out false
% 0.16/0.51 % --bmc1_verbose false
% 0.16/0.51 % --bmc1_dump_clauses_tptp false
% 2.42/3.00 % --bmc1_dump_unsat_core_tptp false
% 2.42/3.00 % --bmc1_dump_file -
% 2.42/3.00 % --bmc1_ucm_expand_uc_limit 128
% 2.42/3.00 % --bmc1_ucm_n_expand_iterations 6
% 2.42/3.00 % --bmc1_ucm_extend_mode 1
% 2.42/3.00 % --bmc1_ucm_init_mode 2
% 2.42/3.00 % --bmc1_ucm_cone_mode none
% 2.42/3.00 % --bmc1_ucm_reduced_relation_type 0
% 2.42/3.00 % --bmc1_ucm_relax_model 4
% 2.42/3.00 % --bmc1_ucm_full_tr_after_sat true
% 2.42/3.00 % --bmc1_ucm_expand_neg_assumptions false
% 2.42/3.00 % --bmc1_ucm_layered_model none
% 2.42/3.00 % --bmc1_ucm_max_lemma_size 10
% 2.42/3.00
% 2.42/3.00 % ------ AIG Options
% 2.42/3.00
% 2.42/3.00 % --aig_mode false
% 2.42/3.00
% 2.42/3.00 % ------ Instantiation Options
% 2.42/3.00
% 2.42/3.00 % --instantiation_flag true
% 2.42/3.00 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 2.42/3.00 % --inst_solver_per_active 750
% 2.42/3.00 % --inst_solver_calls_frac 0.5
% 2.42/3.00 % --inst_passive_queue_type priority_queues
% 2.42/3.00 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 2.42/3.00 % --inst_passive_queues_freq [25;2]
% 2.42/3.00 % --inst_dismatching true
% 2.42/3.00 % --inst_eager_unprocessed_to_passive true
% 2.42/3.00 % --inst_prop_sim_given true
% 2.42/3.00 % --inst_prop_sim_new false
% 2.42/3.00 % --inst_orphan_elimination true
% 2.42/3.00 % --inst_learning_loop_flag true
% 2.42/3.00 % --inst_learning_start 3000
% 2.42/3.00 % --inst_learning_factor 2
% 2.42/3.00 % --inst_start_prop_sim_after_learn 3
% 2.42/3.00 % --inst_sel_renew solver
% 2.42/3.00 % --inst_lit_activity_flag true
% 2.42/3.00 % --inst_out_proof true
% 2.42/3.00
% 2.42/3.00 % ------ Resolution Options
% 2.42/3.00
% 2.42/3.00 % --resolution_flag true
% 2.42/3.00 % --res_lit_sel kbo_max
% 2.42/3.00 % --res_to_prop_solver none
% 2.42/3.00 % --res_prop_simpl_new false
% 2.42/3.00 % --res_prop_simpl_given false
% 2.42/3.00 % --res_passive_queue_type priority_queues
% 2.42/3.00 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 2.42/3.00 % --res_passive_queues_freq [15;5]
% 2.42/3.00 % --res_forward_subs full
% 2.42/3.00 % --res_backward_subs full
% 2.42/3.00 % --res_forward_subs_resolution true
% 2.42/3.00 % --res_backward_subs_resolution true
% 2.42/3.00 % --res_orphan_elimination false
% 2.42/3.00 % --res_time_limit 1000.
% 2.42/3.00 % --res_out_proof true
% 2.42/3.00 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_d73ac6.s
% 2.42/3.00 % --modulo true
% 2.42/3.00
% 2.42/3.00 % ------ Combination Options
% 2.42/3.00
% 2.42/3.00 % --comb_res_mult 1000
% 2.42/3.00 % --comb_inst_mult 300
% 2.42/3.00 % ------
% 2.42/3.00
% 2.42/3.00 % ------ Parsing...% successful
% 2.42/3.00
% 2.42/3.00 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 2.42/3.00
% 2.42/3.00 % ------ Proving...
% 2.42/3.00 % ------ Problem Properties
% 2.42/3.00
% 2.42/3.00 %
% 2.42/3.00 % EPR false
% 2.42/3.00 % Horn false
% 2.42/3.00 % Has equality true
% 2.42/3.00
% 2.42/3.00 % % ------ Input Options Time Limit: Unbounded
% 2.42/3.00
% 2.42/3.00
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 Compiling...
% 2.42/3.00 Loading plugin: done.
% 2.42/3.00 % % ------ Current options:
% 2.42/3.00
% 2.42/3.00 % ------ Input Options
% 2.42/3.00
% 2.42/3.00 % --out_options all
% 2.42/3.00 % --tptp_safe_out true
% 2.42/3.00 % --problem_path ""
% 2.42/3.00 % --include_path ""
% 2.42/3.00 % --clausifier .//eprover
% 2.42/3.00 % --clausifier_options --tstp-format
% 2.42/3.00 % --stdin false
% 2.42/3.00 % --dbg_backtrace false
% 2.42/3.00 % --dbg_dump_prop_clauses false
% 2.42/3.00 % --dbg_dump_prop_clauses_file -
% 2.42/3.00 % --dbg_out_stat false
% 2.42/3.00
% 2.42/3.00 % ------ General Options
% 2.42/3.00
% 2.42/3.00 % --fof false
% 2.42/3.00 % --time_out_real 150.
% 2.42/3.00 % --time_out_prep_mult 0.2
% 2.42/3.00 % --time_out_virtual -1.
% 2.42/3.00 % --schedule none
% 2.42/3.00 % --ground_splitting input
% 2.42/3.00 % --splitting_nvd 16
% 2.42/3.00 % --non_eq_to_eq false
% 2.42/3.00 % --prep_gs_sim true
% 2.42/3.00 % --prep_unflatten false
% 2.42/3.00 % --prep_res_sim true
% 2.42/3.00 % --prep_upred true
% 2.42/3.00 % --res_sim_input true
% 2.42/3.00 % --clause_weak_htbl true
% 2.42/3.00 % --gc_record_bc_elim false
% 2.42/3.00 % --symbol_type_check false
% 2.42/3.00 % --clausify_out false
% 2.42/3.00 % --large_theory_mode false
% 2.42/3.00 % --prep_sem_filter none
% 2.42/3.00 % --prep_sem_filter_out false
% 2.42/3.00 % --preprocessed_out false
% 2.42/3.00 % --sub_typing false
% 2.42/3.00 % --brand_transform false
% 2.42/3.00 % --pure_diseq_elim true
% 2.42/3.00 % --min_unsat_core false
% 2.42/3.00 % --pred_elim true
% 2.42/3.00 % --add_important_lit false
% 2.42/3.00 % --soft_assumptions false
% 2.42/3.00 % --reset_solvers false
% 2.42/3.00 % --bc_imp_inh []
% 2.42/3.00 % --conj_cone_tolerance 1.5
% 2.42/3.00 % --prolific_symb_bound 500
% 2.42/3.00 % --lt_threshold 2000
% 2.42/3.00
% 2.42/3.00 % ------ SAT Options
% 2.42/3.00
% 2.42/3.00 % --sat_mode false
% 2.42/3.00 % --sat_fm_restart_options ""
% 2.42/3.00 % --sat_gr_def false
% 2.42/3.00 % --sat_epr_types true
% 2.42/3.00 % --sat_non_cyclic_types false
% 2.42/3.00 % --sat_finite_models false
% 2.42/3.00 % --sat_fm_lemmas false
% 2.42/3.00 % --sat_fm_prep false
% 2.42/3.00 % --sat_fm_uc_incr true
% 2.42/3.00 % --sat_out_model small
% 2.42/3.00 % --sat_out_clauses false
% 2.42/3.00
% 2.42/3.00 % ------ QBF Options
% 2.42/3.00
% 2.42/3.00 % --qbf_mode false
% 2.42/3.00 % --qbf_elim_univ true
% 2.42/3.00 % --qbf_sk_in true
% 2.42/3.00 % --qbf_pred_elim true
% 2.42/3.00 % --qbf_split 32
% 2.42/3.00
% 2.42/3.00 % ------ BMC1 Options
% 2.42/3.00
% 2.42/3.00 % --bmc1_incremental false
% 2.42/3.00 % --bmc1_axioms reachable_all
% 2.42/3.00 % --bmc1_min_bound 0
% 2.42/3.00 % --bmc1_max_bound -1
% 2.42/3.00 % --bmc1_max_bound_default -1
% 2.42/3.00 % --bmc1_symbol_reachability true
% 2.42/3.00 % --bmc1_property_lemmas false
% 2.42/3.00 % --bmc1_k_induction false
% 2.42/3.00 % --bmc1_non_equiv_states false
% 2.42/3.00 % --bmc1_deadlock false
% 2.42/3.00 % --bmc1_ucm false
% 2.42/3.00 % --bmc1_add_unsat_core none
% 2.42/3.00 % --bmc1_unsat_core_children false
% 2.42/3.00 % --bmc1_unsat_core_extrapolate_axioms false
% 2.42/3.00 % --bmc1_out_stat full
% 2.42/3.00 % --bmc1_ground_init false
% 2.42/3.00 % --bmc1_pre_inst_next_state false
% 2.42/3.00 % --bmc1_pre_inst_state false
% 2.42/3.00 % --bmc1_pre_inst_reach_state false
% 2.42/3.00 % --bmc1_out_unsat_core false
% 2.42/3.00 % --bmc1_aig_witness_out false
% 2.42/3.00 % --bmc1_verbose false
% 2.42/3.00 % --bmc1_dump_clauses_tptp false
% 2.42/3.00 % --bmc1_dump_unsat_core_tptp false
% 2.42/3.00 % --bmc1_dump_file -
% 2.42/3.00 % --bmc1_ucm_expand_uc_limit 128
% 2.42/3.00 % --bmc1_ucm_n_expand_iterations 6
% 2.42/3.00 % --bmc1_ucm_extend_mode 1
% 2.42/3.00 % --bmc1_ucm_init_mode 2
% 2.42/3.00 % --bmc1_ucm_cone_mode none
% 2.42/3.00 % --bmc1_ucm_reduced_relation_type 0
% 2.42/3.00 % --bmc1_ucm_relax_model 4
% 2.42/3.00 % --bmc1_ucm_full_tr_after_sat true
% 2.42/3.00 % --bmc1_ucm_expand_neg_assumptions false
% 2.42/3.00 % --bmc1_ucm_layered_model none
% 2.42/3.00 % --bmc1_ucm_max_lemma_size 10
% 2.42/3.00
% 2.42/3.00 % ------ AIG Options
% 2.42/3.00
% 2.42/3.00 % --aig_mode false
% 2.42/3.00
% 2.42/3.00 % ------ Instantiation Options
% 7.64/7.99
% 7.64/7.99 % --instantiation_flag true
% 7.64/7.99 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 7.64/7.99 % --inst_solver_per_active 750
% 7.64/7.99 % --inst_solver_calls_frac 0.5
% 7.64/7.99 % --inst_passive_queue_type priority_queues
% 7.64/7.99 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 7.64/7.99 % --inst_passive_queues_freq [25;2]
% 7.64/7.99 % --inst_dismatching true
% 7.64/7.99 % --inst_eager_unprocessed_to_passive true
% 7.64/7.99 % --inst_prop_sim_given true
% 7.64/7.99 % --inst_prop_sim_new false
% 7.64/7.99 % --inst_orphan_elimination true
% 7.64/7.99 % --inst_learning_loop_flag true
% 7.64/7.99 % --inst_learning_start 3000
% 7.64/7.99 % --inst_learning_factor 2
% 7.64/7.99 % --inst_start_prop_sim_after_learn 3
% 7.64/7.99 % --inst_sel_renew solver
% 7.64/7.99 % --inst_lit_activity_flag true
% 7.64/7.99 % --inst_out_proof true
% 7.64/7.99
% 7.64/7.99 % ------ Resolution Options
% 7.64/7.99
% 7.64/7.99 % --resolution_flag true
% 7.64/7.99 % --res_lit_sel kbo_max
% 7.64/7.99 % --res_to_prop_solver none
% 7.64/7.99 % --res_prop_simpl_new false
% 7.64/7.99 % --res_prop_simpl_given false
% 7.64/7.99 % --res_passive_queue_type priority_queues
% 7.64/7.99 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 7.64/7.99 % --res_passive_queues_freq [15;5]
% 7.64/7.99 % --res_forward_subs full
% 7.64/7.99 % --res_backward_subs full
% 7.64/7.99 % --res_forward_subs_resolution true
% 7.64/7.99 % --res_backward_subs_resolution true
% 7.64/7.99 % --res_orphan_elimination false
% 7.64/7.99 % --res_time_limit 1000.
% 7.64/7.99 % --res_out_proof true
% 7.64/7.99 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_d73ac6.s
% 7.64/7.99 % --modulo true
% 7.64/7.99
% 7.64/7.99 % ------ Combination Options
% 7.64/7.99
% 7.64/7.99 % --comb_res_mult 1000
% 7.64/7.99 % --comb_inst_mult 300
% 7.64/7.99 % ------
% 7.64/7.99
% 7.64/7.99
% 7.64/7.99
% 7.64/7.99 % ------ Proving...
% 7.64/7.99 %
% 7.64/7.99
% 7.64/7.99
% 7.64/7.99 % ------ Statistics
% 7.64/8.00
% 7.64/8.00 % ------ General
% 7.64/8.00
% 7.64/8.00 % num_of_input_clauses: 832
% 7.64/8.00 % num_of_input_neg_conjectures: 1
% 7.64/8.00 % num_of_splits: 0
% 7.64/8.00 % num_of_split_atoms: 0
% 7.64/8.00 % num_of_sem_filtered_clauses: 0
% 7.64/8.00 % num_of_subtypes: 0
% 7.64/8.00 % monotx_restored_types: 0
% 7.64/8.00 % sat_num_of_epr_types: 0
% 7.64/8.00 % sat_num_of_non_cyclic_types: 0
% 7.64/8.00 % sat_guarded_non_collapsed_types: 0
% 7.64/8.00 % is_epr: 0
% 7.64/8.00 % is_horn: 0
% 7.64/8.00 % has_eq: 1
% 7.64/8.00 % num_pure_diseq_elim: 0
% 7.64/8.00 % simp_replaced_by: 0
% 7.64/8.00 % res_preprocessed: 2
% 7.64/8.00 % prep_upred: 0
% 7.64/8.00 % prep_unflattend: 0
% 7.64/8.00 % pred_elim_cands: 0
% 7.64/8.00 % pred_elim: 0
% 7.64/8.00 % pred_elim_cl: 0
% 7.64/8.00 % pred_elim_cycles: 0
% 7.64/8.00 % forced_gc_time: 0
% 7.64/8.00 % gc_basic_clause_elim: 0
% 7.64/8.00 % parsing_time: 0.066
% 7.64/8.00 % sem_filter_time: 0.
% 7.64/8.00 % pred_elim_time: 0.
% 7.64/8.00 % out_proof_time: 0.001
% 7.64/8.00 % monotx_time: 0.
% 7.64/8.00 % subtype_inf_time: 0.
% 7.64/8.00 % unif_index_cands_time: 0.01
% 7.64/8.00 % unif_index_add_time: 0.009
% 7.64/8.00 % total_time: 7.508
% 7.64/8.00 % num_of_symbols: 139
% 7.64/8.00 % num_of_terms: 38572
% 7.64/8.00
% 7.64/8.00 % ------ Propositional Solver
% 7.64/8.00
% 7.64/8.00 % prop_solver_calls: 3
% 7.64/8.00 % prop_fast_solver_calls: 3
% 7.64/8.00 % prop_num_of_clauses: 1649
% 7.64/8.00 % prop_preprocess_simplified: 4865
% 7.64/8.00 % prop_fo_subsumed: 0
% 7.64/8.00 % prop_solver_time: 0.
% 7.64/8.00 % prop_fast_solver_time: 0.
% 7.64/8.00 % prop_unsat_core_time: 0.
% 7.64/8.00
% 7.64/8.00 % ------ QBF
% 7.64/8.00
% 7.64/8.00 % qbf_q_res: 0
% 7.64/8.00 % qbf_num_tautologies: 0
% 7.64/8.00 % qbf_prep_cycles: 0
% 7.64/8.01
% 7.64/8.01 % ------ BMC1
% 7.64/8.01
% 7.64/8.01 % bmc1_current_bound: -1
% 7.64/8.01 % bmc1_last_solved_bound: -1
% 7.64/8.01 % bmc1_unsat_core_size: -1
% 7.64/8.01 % bmc1_unsat_core_parents_size: -1
% 7.64/8.01 % bmc1_merge_next_fun: 0
% 7.64/8.01 % bmc1_unsat_core_clauses_time: 0.
% 7.64/8.01
% 7.64/8.01 % ------ Instantiation
% 7.64/8.01
% 7.64/8.01 % inst_num_of_clauses: 1163
% 7.64/8.01 % inst_num_in_passive: 727
% 7.64/8.01 % inst_num_in_active: 413
% 7.64/8.01 % inst_num_in_unprocessed: 21
% 7.64/8.01 % inst_num_of_loops: 415
% 7.64/8.01 % inst_num_of_learning_restarts: 0
% 7.64/8.01 % inst_num_moves_active_passive: 0
% 7.64/8.01 % inst_lit_activity: 96
% 7.64/8.01 % inst_lit_activity_moves: 0
% 7.64/8.01 % inst_num_tautologies: 0
% 7.64/8.01 % inst_num_prop_implied: 0
% 7.64/8.01 % inst_num_existing_simplified: 0
% 7.64/8.01 % inst_num_eq_res_simplified: 0
% 7.64/8.01 % inst_num_child_elim: 0
% 7.64/8.01 % inst_num_of_dismatching_blockings: 8
% 7.64/8.01 % inst_num_of_non_proper_insts: 391
% 7.64/8.01 % inst_num_of_duplicates: 683
% 7.64/8.01 % inst_inst_num_from_inst_to_res: 0
% 7.64/8.01 % inst_dismatching_checking_time: 0.001
% 7.64/8.01
% 7.64/8.01 % ------ Resolution
% 7.64/8.01
% 7.64/8.01 % res_num_of_clauses: 10275
% 7.64/8.01 % res_num_in_passive: 8538
% 7.64/8.01 % res_num_in_active: 1236
% 7.64/8.01 % res_num_of_loops: 2000
% 7.64/8.01 % res_forward_subset_subsumed: 3418
% 7.64/8.01 % res_backward_subset_subsumed: 0
% 7.64/8.01 % res_forward_subsumed: 1079
% 7.64/8.01 % res_backward_subsumed: 1
% 7.64/8.01 % res_forward_subsumption_resolution: 0
% 7.64/8.01 % res_backward_subsumption_resolution: 0
% 7.64/8.01 % res_clause_to_clause_subsumption: 12567
% 7.64/8.01 % res_orphan_elimination: 0
% 7.64/8.01 % res_tautology_del: 80
% 7.64/8.01 % res_num_eq_res_simplified: 0
% 7.64/8.01 % res_num_sel_changes: 0
% 7.64/8.01 % res_moves_from_active_to_pass: 0
% 7.64/8.01
% 7.64/8.01 % Status Unsatisfiable
% 7.64/8.01 % SZS status Unsatisfiable
% 7.64/8.01 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------