TSTP Solution File: LCL817-1 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : LCL817-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 11:40:15 EDT 2022
% Result : Unsatisfiable 3.37s 3.65s
% Output : CNFRefutation 3.37s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% 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__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
input ).
fof(clsarity_nat__Nat_Osemiring__char__0_0,plain,
( class_Nat_Osemiring__char__0(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Nat_Osemiring__char__0]) ).
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__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Osemiring__1_0,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__1]) ).
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_CHAINED_0_01,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
input ).
fof(cls_CHAINED_0_01_0,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____)
| $false ),
inference(orientation,[status(thm)],[cls_CHAINED_0_01]) ).
cnf(cls_CHAINED_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
input ).
fof(cls_CHAINED_0_0,plain,
( c_Type_Otyping(v_e____,v_u____,v_T____)
| $false ),
inference(orientation,[status(thm)],[cls_CHAINED_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_uIT_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
input ).
fof(cls_uIT_0_0,plain,
( hBOOL(hAPP(c_InductTermi_OIT,v_u____))
| $false ),
inference(orientation,[status(thm)],[cls_uIT_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_True_0,axiom,
v_n____ = v_i____,
input ).
fof(cls_True_0_0,plain,
( v_n____ = v_i____
| $false ),
inference(orientation,[status(thm)],[cls_True_0]) ).
cnf(cls_argT_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
input ).
fof(cls_argT_0_0,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____)
| $false ),
inference(orientation,[status(thm)],[cls_argT_0]) ).
cnf(cls_uT_H_0,axiom,
c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
input ).
fof(cls_uT_H_0_0,plain,
( c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| $false ),
inference(orientation,[status(thm)],[cls_uT_H_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_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_uT_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
input ).
fof(cls_uT_0_0,plain,
( c_Type_Otyping(v_e____,v_u____,v_T____)
| $false ),
inference(orientation,[status(thm)],[cls_uT_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_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_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_shift__eq_0,axiom,
hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T,
input ).
fof(cls_shift__eq_0_0,plain,
! [T_a,V_T,V_e,V_x] :
( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T
| $false ),
inference(orientation,[status(thm)],[cls_shift__eq_0]) ).
cnf(cls_Var__IT_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))),
input ).
fof(cls_Var__IT_0_0,plain,
! [V_n] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n)))
| $false ),
inference(orientation,[status(thm)],[cls_Var__IT_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_Var_I2_J_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______),
input ).
fof(cls_Var_I2_J_0_0,plain,
( c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______)
| $false ),
inference(orientation,[status(thm)],[cls_Var_I2_J_0]) ).
cnf(cls_varT_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
input ).
fof(cls_varT_0_0,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| $false ),
inference(orientation,[status(thm)],[cls_varT_0]) ).
cnf(cls_headT_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
input ).
fof(cls_headT_0_0,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))
| $false ),
inference(orientation,[status(thm)],[cls_headT_0]) ).
cnf(cls_argsT_0,axiom,
c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
input ).
fof(cls_argsT_0_0,plain,
( c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____)
| $false ),
inference(orientation,[status(thm)],[cls_argsT_0]) ).
cnf(cls_nT_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
input ).
fof(cls_nT_0_0,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| $false ),
inference(orientation,[status(thm)],[cls_nT_0]) ).
cnf(cls_T_0,axiom,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
input ).
fof(cls_T_0_0,plain,
( v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))
| $false ),
inference(orientation,[status(thm)],[cls_T_0]) ).
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_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_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_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_Cons_0,axiom,
v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),
input ).
fof(cls_Cons_0_0,plain,
( v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB)
| $false ),
inference(orientation,[status(thm)],[cls_Cons_0]) ).
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_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_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_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_Var_I4_J_0,axiom,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
input ).
fof(cls_Var_I4_J_0_0,plain,
( c_Type_Otyping(v_ea______,v_ua______,v_T____)
| $false ),
inference(orientation,[status(thm)],[cls_Var_I4_J_0]) ).
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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_Var_I3_J_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
input ).
fof(cls_Var_I3_J_0_0,plain,
( hBOOL(hAPP(c_InductTermi_OIT,v_ua______))
| $false ),
inference(orientation,[status(thm)],[cls_Var_I3_J_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]) ).
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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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__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__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]) ).
fof(def_lhs_atom1,axiom,
! [V_xs,V_x,V_ts,T_a] :
( lhs_atom1(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_0,plain,
! [T_a,V_ts,V_x,V_xs] :
( lhs_atom1(V_xs,V_x,V_ts,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__append__conv2_5_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [V_zs,V_ys,V_x,T_a] :
( lhs_atom2(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_1,plain,
! [T_a,V_x,V_ys,V_zs] :
( lhs_atom2(V_zs,V_ys,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__append__conv2_4_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [V_xs1,V_xs,V_us,T_a] :
( lhs_atom3(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_2,plain,
! [T_a,V_us,V_xs,V_xs1] :
( lhs_atom3(V_xs1,V_xs,V_us,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__appendI_0_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [V_zs,V_ys,V_xs,T_a] :
( lhs_atom4(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_3,plain,
! [T_a,V_xs,V_ys,V_zs] :
( lhs_atom4(V_zs,V_ys,V_xs,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__assoc_0_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [T_a] :
( lhs_atom5(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_4,plain,
! [T_a] :
( lhs_atom5(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__is__Nil__conv_2_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [V_xs,V_x,T_a] :
( lhs_atom6(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_5,plain,
! [T_a,V_x,V_xs] :
( lhs_atom6(V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__Cons__conv_4_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [V_ys,V_xs,V_f,V_a,T_b,T_a] :
( lhs_atom7(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_6,plain,
! [T_a,T_b,V_a,V_f,V_xs,V_ys] :
( lhs_atom7(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_atom7]) ).
fof(def_lhs_atom8,axiom,
! [V_ys,T_a] :
( lhs_atom8(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_7,plain,
! [T_a,V_ys] :
( lhs_atom8(V_ys,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_self__append__conv2_1_0,def_lhs_atom8]) ).
fof(to_be_clausified_8,plain,
! [T_a,V_ys] :
( lhs_atom8(V_ys,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__Nil_0_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [V_xs,T_a] :
( lhs_atom9(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_9,plain,
! [T_a,V_xs] :
( lhs_atom9(V_xs,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_self__append__conv_1_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [V_x,T_a] :
( lhs_atom10(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_10,plain,
! [T_a,V_x] :
( lhs_atom10(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_eq__Nil__appendI_0_0,def_lhs_atom10]) ).
fof(to_be_clausified_11,plain,
! [T_a,V_xs] :
( lhs_atom9(V_xs,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__Nil2_0_0,def_lhs_atom9]) ).
fof(def_lhs_atom11,axiom,
! [V_zs,V_xa,V_x,T_a] :
( lhs_atom11(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_12,plain,
! [T_a,V_x,V_xa,V_zs] :
( lhs_atom11(V_zs,V_xa,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__eq__Cons__conv_5_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [V_ys,V_xs,V_x,T_a] :
( lhs_atom12(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_13,plain,
! [T_a,V_x,V_xs,V_ys] :
( lhs_atom12(V_ys,V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_append__Cons_0_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [V_zs,V_xa,V_x,T_a] :
( lhs_atom13(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_14,plain,
! [T_a,V_x,V_xa,V_zs] :
( lhs_atom13(V_zs,V_xa,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Cons__eq__append__conv_5_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [V_zs,V_xs1,V_x,T_a] :
( lhs_atom14(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_15,plain,
! [T_a,V_x,V_xs1,V_zs] :
( lhs_atom14(V_zs,V_xs1,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Cons__eq__appendI_0_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [V_xs,V_x,T_a] :
( lhs_atom15(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_16,plain,
! [T_a,V_x,V_xs] :
( lhs_atom15(V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Cons__eq__append__conv_4_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [T_a] :
( lhs_atom16(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_17,plain,
! [T_a] :
( lhs_atom16(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nil__is__append__conv_2_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [V_ys,V_xs,V_f,V_a,T_b,T_a] :
( lhs_atom17(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_18,plain,
! [T_a,T_b,V_a,V_f,V_xs,V_ys] :
( lhs_atom17(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_atom17]) ).
fof(def_lhs_atom18,axiom,
! [V_xs,V_x,T_a] :
( lhs_atom18(V_xs,V_x,T_a)
<=> V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
! [T_a,V_x,V_xs] :
( lhs_atom18(V_xs,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__Cons__self_0_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [V_x,V_t,T_a] :
( lhs_atom19(V_x,V_t,T_a)
<=> c_List_Olist_OCons(V_x,V_t,T_a) != V_t ),
inference(definition,[],]) ).
fof(to_be_clausified_20,plain,
! [T_a,V_t,V_x] :
( lhs_atom19(V_x,V_t,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__Cons__self2_0_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [V_list_H,V_a_H,T_a] :
( lhs_atom20(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_21,plain,
! [T_a,V_a_H,V_list_H] :
( lhs_atom20(V_list_H,V_a_H,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_list_Osimps_I3_J_0_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [V_xa,V_x,T_a] :
( lhs_atom21(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_22,plain,
! [T_a,V_x,V_xa] :
( lhs_atom21(V_xa,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_neq__Nil__conv_1_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [V_xs,V_x,V_f,V_a,T_b,T_a] :
( lhs_atom22(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_23,plain,
! [T_a,T_b,V_a,V_f,V_x,V_xs] :
( lhs_atom22(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_atom22]) ).
fof(def_lhs_atom23,axiom,
! [V_f,V_a,T_b,T_a] :
( lhs_atom23(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_24,plain,
! [T_a,T_b,V_a,V_f] :
( lhs_atom23(V_f,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_foldr_Osimps_I1_J_0_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
( lhs_atom24
<=> hBOOL(hAPP(c_InductTermi_OIT,v_ua______)) ),
inference(definition,[],]) ).
fof(to_be_clausified_25,plain,
( lhs_atom24
| $false ),
inference(fold_definition,[status(thm)],[cls_Var_I3_J_0_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [V_A,T_a] :
( lhs_atom25(V_A,T_a)
<=> c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
! [T_a,V_A] :
( lhs_atom25(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_listsp_ONil_0_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [V_xs,V_r,T_a] :
( lhs_atom26(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_27,plain,
! [T_a,V_r,V_xs] :
( lhs_atom26(V_xs,V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__Nil__step1_0_0,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [V_xs,V_r,T_a] :
( lhs_atom27(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_28,plain,
! [T_a,V_r,V_xs] :
( lhs_atom27(V_xs,V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__step1__Nil_0_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [V_f,V_a,T_b,T_a] :
( lhs_atom28(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_29,plain,
! [T_a,T_b,V_a,V_f] :
( lhs_atom28(V_f,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_foldl__Nil_0_0,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [T_a] :
( lhs_atom29(T_a)
<=> c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_30,plain,
! [T_a] :
( lhs_atom29(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_conversep__eq_0_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [V_list_H,V_a_H,T_a] :
( lhs_atom30(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_31,plain,
! [T_a,V_a_H,V_list_H] :
( lhs_atom30(V_list_H,V_a_H,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_list_Osimps_I2_J_0_0,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
! [V_xs,V_x,V_f,V_a,T_b,T_a] :
( lhs_atom31(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_32,plain,
! [T_a,T_b,V_a,V_f,V_x,V_xs] :
( lhs_atom31(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_atom31]) ).
fof(def_lhs_atom32,axiom,
! [V_r,T_b,T_a] :
( lhs_atom32(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_33,plain,
! [T_a,T_b,V_r] :
( lhs_atom32(V_r,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_conversep__conversep_0_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
! [V_u,V_ts,V_t] :
( lhs_atom33(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_34,plain,
! [V_t,V_ts,V_u] :
( lhs_atom33(V_u,V_ts,V_t)
| $false ),
inference(fold_definition,[status(thm)],[cls_app__last_0_0,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [V_s,V_r] :
( lhs_atom34(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_35,plain,
! [V_r,V_s] :
( lhs_atom34(V_s,V_r)
| $false ),
inference(fold_definition,[status(thm)],[cls_App__eq__foldl__conv_4_0,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [V_nat,V_dB_H] :
( lhs_atom35(V_nat,V_dB_H)
<=> c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_36,plain,
! [V_dB_H,V_nat] :
( lhs_atom35(V_nat,V_dB_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I7_J_0_0,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
! [V_dB_H,V_dB2,V_dB1] :
( lhs_atom36(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_37,plain,
! [V_dB1,V_dB2,V_dB_H] :
( lhs_atom36(V_dB_H,V_dB2,V_dB1)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I8_J_0_0,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
! [V_dB_H,V_dB2,V_dB1] :
( lhs_atom37(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_38,plain,
! [V_dB1,V_dB2,V_dB_H] :
( lhs_atom37(V_dB_H,V_dB2,V_dB1)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I9_J_0_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
( lhs_atom38
<=> ~ 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_39,plain,
( lhs_atom38
| $false ),
inference(fold_definition,[status(thm)],[cls_neq0__conv_1_0,def_lhs_atom38]) ).
fof(def_lhs_atom39,axiom,
! [V_n] :
( lhs_atom39(V_n)
<=> ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_40,plain,
! [V_n] :
( lhs_atom39(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_less__not__refl_0_0,def_lhs_atom39]) ).
fof(def_lhs_atom40,axiom,
! [V_x] :
( lhs_atom40(V_x)
<=> ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_41,plain,
! [V_x] :
( lhs_atom40(V_x)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__less__le_1_0,def_lhs_atom40]) ).
fof(def_lhs_atom41,axiom,
! [V_ts,V_ss,V_r,V_n] :
( lhs_atom41(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_42,plain,
! [V_n,V_r,V_ss,V_ts] :
( lhs_atom41(V_ts,V_ss,V_r,V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Var__apps__neq__Abs__apps_0_0,def_lhs_atom41]) ).
fof(def_lhs_atom42,axiom,
! [V_nat,V_dB_H] :
( lhs_atom42(V_nat,V_dB_H)
<=> c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ),
inference(definition,[],]) ).
fof(to_be_clausified_43,plain,
! [V_dB_H,V_nat] :
( lhs_atom42(V_nat,V_dB_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I6_J_0_0,def_lhs_atom42]) ).
fof(def_lhs_atom43,axiom,
! [V_x,V_r,T_a] :
( lhs_atom43(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_44,plain,
! [T_a,V_r,V_x] :
( lhs_atom43(V_x,V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nitpick_Ortranclp__def_1_0,def_lhs_atom43]) ).
fof(def_lhs_atom44,axiom,
! [V_r,V_a,T_a] :
( lhs_atom44(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_45,plain,
! [T_a,V_a,V_r] :
( lhs_atom44(V_r,V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtranclp_Ortrancl__refl_0_0,def_lhs_atom44]) ).
fof(def_lhs_atom45,axiom,
( lhs_atom45
<=> c_Type_Otyping(v_ea______,v_ua______,v_T____) ),
inference(definition,[],]) ).
fof(to_be_clausified_46,plain,
( lhs_atom45
| $false ),
inference(fold_definition,[status(thm)],[cls_Var_I4_J_0_0,def_lhs_atom45]) ).
fof(def_lhs_atom46,axiom,
! [V_m] :
( lhs_atom46(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_47,plain,
! [V_m] :
( lhs_atom46(V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_Var__eq__apps__conv_2_0,def_lhs_atom46]) ).
fof(def_lhs_atom47,axiom,
! [V_m] :
( lhs_atom47(V_m)
<=> ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_48,plain,
! [V_m] :
( lhs_atom47(V_m)
| $false ),
inference(fold_definition,[status(thm)],[cls_gr__implies__not0_0_0,def_lhs_atom47]) ).
fof(def_lhs_atom48,axiom,
! [V_n] :
( lhs_atom48(V_n)
<=> ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_49,plain,
! [V_n] :
( lhs_atom48(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__less0_0_0,def_lhs_atom48]) ).
fof(def_lhs_atom49,axiom,
! [V_r] :
( lhs_atom49(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_50,plain,
! [V_r] :
( lhs_atom49(V_r)
| $false ),
inference(fold_definition,[status(thm)],[cls_Abs__eq__apps__conv_2_0,def_lhs_atom49]) ).
fof(def_lhs_atom50,axiom,
( lhs_atom50
<=> v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB) ),
inference(definition,[],]) ).
fof(to_be_clausified_51,plain,
( lhs_atom50
| $false ),
inference(fold_definition,[status(thm)],[cls_Cons_0_0,def_lhs_atom50]) ).
fof(def_lhs_atom51,axiom,
! [V_r] :
( lhs_atom51(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_52,plain,
! [V_r] :
( lhs_atom51(V_r)
| $false ),
inference(fold_definition,[status(thm)],[cls_apps__eq__Abs__conv_2_0,def_lhs_atom51]) ).
fof(def_lhs_atom52,axiom,
! [V_t,V_ss,V_s,V_n] :
( lhs_atom52(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_53,plain,
! [V_n,V_s,V_ss,V_t] :
( lhs_atom52(V_t,V_ss,V_s,V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Abs__App__neq__Var__apps_0_0,def_lhs_atom52]) ).
fof(def_lhs_atom53,axiom,
! [V_r,T_a] :
( lhs_atom53(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_54,plain,
! [T_a,V_r] :
( lhs_atom53(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtranclp__idemp_0_0,def_lhs_atom53]) ).
fof(def_lhs_atom54,axiom,
! [V_nat,V_dB2_H,V_dB1_H] :
( lhs_atom54(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_55,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( lhs_atom54(V_nat,V_dB2_H,V_dB1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I5_J_0_0,def_lhs_atom54]) ).
fof(def_lhs_atom55,axiom,
( lhs_atom55
<=> v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ),
inference(definition,[],]) ).
fof(to_be_clausified_56,plain,
( lhs_atom55
| $false ),
inference(fold_definition,[status(thm)],[cls_T_0_0,def_lhs_atom55]) ).
fof(def_lhs_atom56,axiom,
( lhs_atom56
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ),
inference(definition,[],]) ).
fof(to_be_clausified_57,plain,
( lhs_atom56
| $false ),
inference(fold_definition,[status(thm)],[cls_nT_0_0,def_lhs_atom56]) ).
fof(def_lhs_atom57,axiom,
( lhs_atom57
<=> c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____) ),
inference(definition,[],]) ).
fof(to_be_clausified_58,plain,
( lhs_atom57
| $false ),
inference(fold_definition,[status(thm)],[cls_argsT_0_0,def_lhs_atom57]) ).
fof(def_lhs_atom58,axiom,
( lhs_atom58
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ),
inference(definition,[],]) ).
fof(to_be_clausified_59,plain,
( lhs_atom58
| $false ),
inference(fold_definition,[status(thm)],[cls_headT_0_0,def_lhs_atom58]) ).
fof(def_lhs_atom59,axiom,
( lhs_atom59
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
inference(definition,[],]) ).
fof(to_be_clausified_60,plain,
( lhs_atom59
| $false ),
inference(fold_definition,[status(thm)],[cls_varT_0_0,def_lhs_atom59]) ).
fof(def_lhs_atom60,axiom,
( lhs_atom60
<=> c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______) ),
inference(definition,[],]) ).
fof(to_be_clausified_61,plain,
( lhs_atom60
| $false ),
inference(fold_definition,[status(thm)],[cls_Var_I2_J_0_0,def_lhs_atom60]) ).
fof(def_lhs_atom61,axiom,
! [V_t,V_s,V_k] :
( lhs_atom61(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_62,plain,
! [V_k,V_s,V_t] :
( lhs_atom61(V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_lift_Osimps_I2_J_0_0,def_lhs_atom61]) ).
fof(def_lhs_atom62,axiom,
! [V_n] :
( lhs_atom62(V_n)
<=> hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))) ),
inference(definition,[],]) ).
fof(to_be_clausified_63,plain,
! [V_n] :
( lhs_atom62(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Var__IT_0_0,def_lhs_atom62]) ).
fof(def_lhs_atom63,axiom,
! [V_x,V_e,V_T,T_a] :
( lhs_atom63(V_x,V_e,V_T,T_a)
<=> hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ),
inference(definition,[],]) ).
fof(to_be_clausified_64,plain,
! [T_a,V_T,V_e,V_x] :
( lhs_atom63(V_x,V_e,V_T,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_shift__eq_0_0,def_lhs_atom63]) ).
fof(def_lhs_atom64,axiom,
! [V_nat,V_dB2_H,V_dB1_H] :
( lhs_atom64(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_65,plain,
! [V_dB1_H,V_dB2_H,V_nat] :
( lhs_atom64(V_nat,V_dB2_H,V_dB1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_dB_Osimps_I4_J_0_0,def_lhs_atom64]) ).
fof(def_lhs_atom65,axiom,
! [V_t,V_s] :
( lhs_atom65(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_66,plain,
! [V_s,V_t] :
( lhs_atom65(V_t,V_s)
| $false ),
inference(fold_definition,[status(thm)],[cls_beta_0_0,def_lhs_atom65]) ).
fof(def_lhs_atom66,axiom,
! [V_t,V_i] :
( lhs_atom66(V_t,V_i)
<=> ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)) ),
inference(definition,[],]) ).
fof(to_be_clausified_67,plain,
! [V_i,V_t] :
( lhs_atom66(V_t,V_i)
| $false ),
inference(fold_definition,[status(thm)],[cls_beta__cases_I1_J_0_0,def_lhs_atom66]) ).
fof(def_lhs_atom67,axiom,
( lhs_atom67
<=> c_Type_Otyping(v_e____,v_u____,v_T____) ),
inference(definition,[],]) ).
fof(to_be_clausified_68,plain,
( lhs_atom67
| $false ),
inference(fold_definition,[status(thm)],[cls_uT_0_0,def_lhs_atom67]) ).
fof(def_lhs_atom68,axiom,
! [V_u,V_t,V_s,V_k] :
( lhs_atom68(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_69,plain,
! [V_k,V_s,V_t,V_u] :
( lhs_atom68(V_u,V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__App_0_0,def_lhs_atom68]) ).
fof(def_lhs_atom69,axiom,
! [V_u,V_k] :
( lhs_atom69(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_70,plain,
! [V_k,V_u] :
( lhs_atom69(V_u,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__eq_0_0,def_lhs_atom69]) ).
fof(def_lhs_atom70,axiom,
( lhs_atom70
<=> c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
inference(definition,[],]) ).
fof(to_be_clausified_71,plain,
( lhs_atom70
| $false ),
inference(fold_definition,[status(thm)],[cls_uT_H_0_0,def_lhs_atom70]) ).
fof(def_lhs_atom71,axiom,
( lhs_atom71
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____) ),
inference(definition,[],]) ).
fof(to_be_clausified_72,plain,
( lhs_atom71
| $false ),
inference(fold_definition,[status(thm)],[cls_argT_0_0,def_lhs_atom71]) ).
fof(def_lhs_atom72,axiom,
( lhs_atom72
<=> v_n____ = v_i____ ),
inference(definition,[],]) ).
fof(to_be_clausified_73,plain,
( lhs_atom72
| $false ),
inference(fold_definition,[status(thm)],[cls_True_0_0,def_lhs_atom72]) ).
fof(def_lhs_atom73,axiom,
! [V_x,V_env] :
( lhs_atom73(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_74,plain,
! [V_env,V_x] :
( lhs_atom73(V_x,V_env)
| $false ),
inference(fold_definition,[status(thm)],[cls_typing_OVar_0_0,def_lhs_atom73]) ).
fof(def_lhs_atom74,axiom,
( lhs_atom74
<=> hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ),
inference(definition,[],]) ).
fof(to_be_clausified_75,plain,
( lhs_atom74
| $false ),
inference(fold_definition,[status(thm)],[cls_uIT_0_0,def_lhs_atom74]) ).
fof(def_lhs_atom75,axiom,
! [V_t,V_s,V_k] :
( lhs_atom75(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_76,plain,
! [V_k,V_s,V_t] :
( lhs_atom75(V_t,V_s,V_k)
| $false ),
inference(fold_definition,[status(thm)],[cls_subst__lift_0_0,def_lhs_atom75]) ).
fof(to_be_clausified_77,plain,
( lhs_atom67
| $false ),
inference(fold_definition,[status(thm)],[cls_CHAINED_0_0,def_lhs_atom67]) ).
fof(to_be_clausified_78,plain,
( lhs_atom71
| $false ),
inference(fold_definition,[status(thm)],[cls_CHAINED_0_01_0,def_lhs_atom71]) ).
fof(def_lhs_atom76,axiom,
( lhs_atom76
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_79,plain,
( lhs_atom76
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add_0,def_lhs_atom76]) ).
fof(def_lhs_atom77,axiom,
( lhs_atom77
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_80,plain,
( lhs_atom77
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,def_lhs_atom77]) ).
fof(def_lhs_atom78,axiom,
( lhs_atom78
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_81,plain,
( lhs_atom78
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__comm__monoid__add_0,def_lhs_atom78]) ).
fof(def_lhs_atom79,axiom,
( lhs_atom79
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_82,plain,
( lhs_atom79
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add_0,def_lhs_atom79]) ).
fof(def_lhs_atom80,axiom,
( lhs_atom80
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_83,plain,
( lhs_atom80
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__semigroup__add_0,def_lhs_atom80]) ).
fof(def_lhs_atom81,axiom,
( lhs_atom81
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_84,plain,
( lhs_atom81
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom_0,def_lhs_atom81]) ).
fof(def_lhs_atom82,axiom,
( lhs_atom82
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_85,plain,
( lhs_atom82
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1_0,def_lhs_atom82]) ).
fof(def_lhs_atom83,axiom,
( lhs_atom83
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_86,plain,
( lhs_atom83
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__add_0,def_lhs_atom83]) ).
fof(def_lhs_atom84,axiom,
( lhs_atom84
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_87,plain,
( lhs_atom84
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__add_0,def_lhs_atom84]) ).
fof(def_lhs_atom85,axiom,
( lhs_atom85
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_88,plain,
( lhs_atom85
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Osemigroup__add_0,def_lhs_atom85]) ).
fof(def_lhs_atom86,axiom,
( lhs_atom86
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_89,plain,
( lhs_atom86
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__1_0,def_lhs_atom86]) ).
fof(def_lhs_atom87,axiom,
( lhs_atom87
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_90,plain,
( lhs_atom87
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add_0,def_lhs_atom87]) ).
fof(def_lhs_atom88,axiom,
( lhs_atom88
<=> class_Nat_Osemiring__char__0(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_91,plain,
( lhs_atom88
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Nat_Osemiring__char__0_0,def_lhs_atom88]) ).
fof(def_lhs_atom89,axiom,
( lhs_atom89
<=> class_Orderings_Opreorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_92,plain,
( lhs_atom89
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Opreorder_0,def_lhs_atom89]) ).
fof(def_lhs_atom90,axiom,
( lhs_atom90
<=> class_Orderings_Olinorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_93,plain,
( lhs_atom90
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Olinorder_0,def_lhs_atom90]) ).
fof(def_lhs_atom91,axiom,
( lhs_atom91
<=> class_Orderings_Oorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_94,plain,
( lhs_atom91
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Oorder_0,def_lhs_atom91]) ).
fof(def_lhs_atom92,axiom,
( lhs_atom92
<=> class_Orderings_Opreorder(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_95,plain,
( lhs_atom92
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Opreorder_0,def_lhs_atom92]) ).
fof(def_lhs_atom93,axiom,
( lhs_atom93
<=> class_Orderings_Oorder(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_96,plain,
( lhs_atom93
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Oorder_0,def_lhs_atom93]) ).
fof(def_lhs_atom94,axiom,
! [V_x,T_a] :
( lhs_atom94(V_x,T_a)
<=> hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ),
inference(definition,[],]) ).
fof(to_be_clausified_97,plain,
! [T_a,V_x] :
( lhs_atom94(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0_0,def_lhs_atom94]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X1,X2,X9,X10,X11,X4] :
( lhs_atom31(X1,X2,X9,X10,X11,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_1,axiom,
! [X1,X2,X9,X10,X11,X4] :
( lhs_atom22(X1,X2,X9,X10,X11,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_2,axiom,
! [X6,X1,X9,X10,X11,X4] :
( lhs_atom17(X6,X1,X9,X10,X11,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_3,axiom,
! [X6,X1,X9,X10,X11,X4] :
( lhs_atom7(X6,X1,X9,X10,X11,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_4,axiom,
! [X18,X13,X19,X29] :
( lhs_atom68(X18,X13,X19,X29)
| ~ $true ),
file('<stdin>',to_be_clausified_69) ).
fof(c_0_5,axiom,
! [X2,X30,X31,X4] :
( lhs_atom63(X2,X30,X31,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_64) ).
fof(c_0_6,axiom,
! [X13,X25,X19,X24] :
( lhs_atom52(X13,X25,X19,X24)
| ~ $true ),
file('<stdin>',to_be_clausified_53) ).
fof(c_0_7,axiom,
! [X3,X25,X17,X24] :
( lhs_atom41(X3,X25,X17,X24)
| ~ $true ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_8,axiom,
! [X9,X10,X11,X4] :
( lhs_atom28(X9,X10,X11,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_9,axiom,
! [X9,X10,X11,X4] :
( lhs_atom23(X9,X10,X11,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_10,axiom,
! [X5,X7,X2,X4] :
( lhs_atom14(X5,X7,X2,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_11,axiom,
! [X5,X12,X2,X4] :
( lhs_atom13(X5,X12,X2,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_12,axiom,
! [X6,X1,X2,X4] :
( lhs_atom12(X6,X1,X2,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_13,axiom,
! [X5,X12,X2,X4] :
( lhs_atom11(X5,X12,X2,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_14,axiom,
! [X5,X6,X1,X4] :
( lhs_atom4(X5,X6,X1,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_15,axiom,
! [X7,X1,X8,X4] :
( lhs_atom3(X7,X1,X8,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_16,axiom,
! [X5,X6,X2,X4] :
( lhs_atom2(X5,X6,X2,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_17,axiom,
! [X1,X2,X3,X4] :
( lhs_atom1(X1,X2,X3,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_18,axiom,
! [X13,X19,X29] :
( lhs_atom75(X13,X19,X29)
| ~ $true ),
file('<stdin>',to_be_clausified_76) ).
fof(c_0_19,axiom,
! [X20,X27,X28] :
( lhs_atom64(X20,X27,X28)
| ~ $true ),
file('<stdin>',to_be_clausified_65) ).
fof(c_0_20,axiom,
! [X13,X19,X29] :
( lhs_atom61(X13,X19,X29)
| ~ $true ),
file('<stdin>',to_be_clausified_62) ).
fof(c_0_21,axiom,
! [X20,X27,X28] :
( lhs_atom54(X20,X27,X28)
| ~ $true ),
file('<stdin>',to_be_clausified_55) ).
fof(c_0_22,axiom,
! [X17,X10,X4] :
( lhs_atom44(X17,X10,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_23,axiom,
! [X2,X17,X4] :
( lhs_atom43(X2,X17,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_24,axiom,
! [X21,X22,X23] :
( lhs_atom37(X21,X22,X23)
| ~ $true ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_25,axiom,
! [X21,X22,X23] :
( lhs_atom36(X21,X22,X23)
| ~ $true ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_26,axiom,
! [X18,X3,X13] :
( lhs_atom33(X18,X3,X13)
| ~ $true ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_27,axiom,
! [X17,X11,X4] :
( lhs_atom32(X17,X11,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_28,axiom,
! [X14,X15,X4] :
( lhs_atom30(X14,X15,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_29,axiom,
! [X1,X17,X4] :
( lhs_atom27(X1,X17,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_30,axiom,
! [X1,X17,X4] :
( lhs_atom26(X1,X17,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_31,axiom,
! [X12,X2,X4] :
( lhs_atom21(X12,X2,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_32,axiom,
! [X14,X15,X4] :
( lhs_atom20(X14,X15,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_33,axiom,
! [X2,X13,X4] :
( lhs_atom19(X2,X13,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_34,axiom,
! [X1,X2,X4] :
( lhs_atom18(X1,X2,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_35,axiom,
! [X1,X2,X4] :
( lhs_atom15(X1,X2,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_36,axiom,
! [X1,X2,X4] :
( lhs_atom6(X1,X2,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_37,axiom,
! [X2,X4] :
( lhs_atom94(X2,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_97) ).
fof(c_0_38,axiom,
! [X2,X33] :
( lhs_atom73(X2,X33)
| ~ $true ),
file('<stdin>',to_be_clausified_74) ).
fof(c_0_39,axiom,
! [X18,X29] :
( lhs_atom69(X18,X29)
| ~ $true ),
file('<stdin>',to_be_clausified_70) ).
fof(c_0_40,axiom,
! [X13,X32] :
( lhs_atom66(X13,X32)
| ~ $true ),
file('<stdin>',to_be_clausified_67) ).
fof(c_0_41,axiom,
! [X13,X19] :
( lhs_atom65(X13,X19)
| ~ $true ),
file('<stdin>',to_be_clausified_66) ).
fof(c_0_42,axiom,
! [X17,X4] :
( lhs_atom53(X17,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_54) ).
fof(c_0_43,axiom,
! [X20,X21] :
( lhs_atom42(X20,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_44,axiom,
! [X20,X21] :
( lhs_atom35(X20,X21)
| ~ $true ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_45,axiom,
! [X19,X17] :
( lhs_atom34(X19,X17)
| ~ $true ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_46,axiom,
! [X16,X4] :
( lhs_atom25(X16,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_47,axiom,
! [X1,X4] :
( lhs_atom9(X1,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_48,axiom,
! [X2,X4] :
( lhs_atom10(X2,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_49,axiom,
! [X1,X4] :
( lhs_atom9(X1,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_50,axiom,
! [X6,X4] :
( lhs_atom8(X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_51,axiom,
! [X6,X4] :
( lhs_atom8(X6,X4)
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_52,axiom,
! [X24] :
( lhs_atom62(X24)
| ~ $true ),
file('<stdin>',to_be_clausified_63) ).
fof(c_0_53,axiom,
! [X17] :
( lhs_atom51(X17)
| ~ $true ),
file('<stdin>',to_be_clausified_52) ).
fof(c_0_54,axiom,
! [X17] :
( lhs_atom49(X17)
| ~ $true ),
file('<stdin>',to_be_clausified_50) ).
fof(c_0_55,axiom,
! [X24] :
( lhs_atom48(X24)
| ~ $true ),
file('<stdin>',to_be_clausified_49) ).
fof(c_0_56,axiom,
! [X26] :
( lhs_atom47(X26)
| ~ $true ),
file('<stdin>',to_be_clausified_48) ).
fof(c_0_57,axiom,
! [X26] :
( lhs_atom46(X26)
| ~ $true ),
file('<stdin>',to_be_clausified_47) ).
fof(c_0_58,axiom,
! [X2] :
( lhs_atom40(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_59,axiom,
! [X24] :
( lhs_atom39(X24)
| ~ $true ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_60,axiom,
! [X4] :
( lhs_atom29(X4)
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_61,axiom,
! [X4] :
( lhs_atom16(X4)
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_62,axiom,
! [X4] :
( lhs_atom5(X4)
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_63,axiom,
( lhs_atom93
| ~ $true ),
file('<stdin>',to_be_clausified_96) ).
fof(c_0_64,axiom,
( lhs_atom92
| ~ $true ),
file('<stdin>',to_be_clausified_95) ).
fof(c_0_65,axiom,
( lhs_atom91
| ~ $true ),
file('<stdin>',to_be_clausified_94) ).
fof(c_0_66,axiom,
( lhs_atom90
| ~ $true ),
file('<stdin>',to_be_clausified_93) ).
fof(c_0_67,axiom,
( lhs_atom89
| ~ $true ),
file('<stdin>',to_be_clausified_92) ).
fof(c_0_68,axiom,
( lhs_atom88
| ~ $true ),
file('<stdin>',to_be_clausified_91) ).
fof(c_0_69,axiom,
( lhs_atom87
| ~ $true ),
file('<stdin>',to_be_clausified_90) ).
fof(c_0_70,axiom,
( lhs_atom86
| ~ $true ),
file('<stdin>',to_be_clausified_89) ).
fof(c_0_71,axiom,
( lhs_atom85
| ~ $true ),
file('<stdin>',to_be_clausified_88) ).
fof(c_0_72,axiom,
( lhs_atom84
| ~ $true ),
file('<stdin>',to_be_clausified_87) ).
fof(c_0_73,axiom,
( lhs_atom83
| ~ $true ),
file('<stdin>',to_be_clausified_86) ).
fof(c_0_74,axiom,
( lhs_atom82
| ~ $true ),
file('<stdin>',to_be_clausified_85) ).
fof(c_0_75,axiom,
( lhs_atom81
| ~ $true ),
file('<stdin>',to_be_clausified_84) ).
fof(c_0_76,axiom,
( lhs_atom80
| ~ $true ),
file('<stdin>',to_be_clausified_83) ).
fof(c_0_77,axiom,
( lhs_atom79
| ~ $true ),
file('<stdin>',to_be_clausified_82) ).
fof(c_0_78,axiom,
( lhs_atom78
| ~ $true ),
file('<stdin>',to_be_clausified_81) ).
fof(c_0_79,axiom,
( lhs_atom77
| ~ $true ),
file('<stdin>',to_be_clausified_80) ).
fof(c_0_80,axiom,
( lhs_atom76
| ~ $true ),
file('<stdin>',to_be_clausified_79) ).
fof(c_0_81,axiom,
( lhs_atom71
| ~ $true ),
file('<stdin>',to_be_clausified_78) ).
fof(c_0_82,axiom,
( lhs_atom67
| ~ $true ),
file('<stdin>',to_be_clausified_77) ).
fof(c_0_83,axiom,
( lhs_atom74
| ~ $true ),
file('<stdin>',to_be_clausified_75) ).
fof(c_0_84,axiom,
( lhs_atom72
| ~ $true ),
file('<stdin>',to_be_clausified_73) ).
fof(c_0_85,axiom,
( lhs_atom71
| ~ $true ),
file('<stdin>',to_be_clausified_72) ).
fof(c_0_86,axiom,
( lhs_atom70
| ~ $true ),
file('<stdin>',to_be_clausified_71) ).
fof(c_0_87,axiom,
( lhs_atom67
| ~ $true ),
file('<stdin>',to_be_clausified_68) ).
fof(c_0_88,axiom,
( lhs_atom60
| ~ $true ),
file('<stdin>',to_be_clausified_61) ).
fof(c_0_89,axiom,
( lhs_atom59
| ~ $true ),
file('<stdin>',to_be_clausified_60) ).
fof(c_0_90,axiom,
( lhs_atom58
| ~ $true ),
file('<stdin>',to_be_clausified_59) ).
fof(c_0_91,axiom,
( lhs_atom57
| ~ $true ),
file('<stdin>',to_be_clausified_58) ).
fof(c_0_92,axiom,
( lhs_atom56
| ~ $true ),
file('<stdin>',to_be_clausified_57) ).
fof(c_0_93,axiom,
( lhs_atom55
| ~ $true ),
file('<stdin>',to_be_clausified_56) ).
fof(c_0_94,axiom,
( lhs_atom50
| ~ $true ),
file('<stdin>',to_be_clausified_51) ).
fof(c_0_95,axiom,
( lhs_atom45
| ~ $true ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_96,axiom,
( lhs_atom38
| ~ $true ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_97,axiom,
( lhs_atom24
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_98,plain,
! [X1,X2,X9,X10,X11,X4] : lhs_atom31(X1,X2,X9,X10,X11,X4),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_99,plain,
! [X1,X2,X9,X10,X11,X4] : lhs_atom22(X1,X2,X9,X10,X11,X4),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_100,plain,
! [X6,X1,X9,X10,X11,X4] : lhs_atom17(X6,X1,X9,X10,X11,X4),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_101,plain,
! [X6,X1,X9,X10,X11,X4] : lhs_atom7(X6,X1,X9,X10,X11,X4),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_102,plain,
! [X18,X13,X19,X29] : lhs_atom68(X18,X13,X19,X29),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_103,plain,
! [X2,X30,X31,X4] : lhs_atom63(X2,X30,X31,X4),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_104,plain,
! [X13,X25,X19,X24] : lhs_atom52(X13,X25,X19,X24),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_105,plain,
! [X3,X25,X17,X24] : lhs_atom41(X3,X25,X17,X24),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_106,plain,
! [X9,X10,X11,X4] : lhs_atom28(X9,X10,X11,X4),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_107,plain,
! [X9,X10,X11,X4] : lhs_atom23(X9,X10,X11,X4),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_108,plain,
! [X5,X7,X2,X4] : lhs_atom14(X5,X7,X2,X4),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_109,plain,
! [X5,X12,X2,X4] : lhs_atom13(X5,X12,X2,X4),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_110,plain,
! [X6,X1,X2,X4] : lhs_atom12(X6,X1,X2,X4),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_111,plain,
! [X5,X12,X2,X4] : lhs_atom11(X5,X12,X2,X4),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_112,plain,
! [X5,X6,X1,X4] : lhs_atom4(X5,X6,X1,X4),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_113,plain,
! [X7,X1,X8,X4] : lhs_atom3(X7,X1,X8,X4),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_114,plain,
! [X5,X6,X2,X4] : lhs_atom2(X5,X6,X2,X4),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_115,plain,
! [X1,X2,X3,X4] : lhs_atom1(X1,X2,X3,X4),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_116,plain,
! [X13,X19,X29] : lhs_atom75(X13,X19,X29),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_117,plain,
! [X20,X27,X28] : lhs_atom64(X20,X27,X28),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_118,plain,
! [X13,X19,X29] : lhs_atom61(X13,X19,X29),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_119,plain,
! [X20,X27,X28] : lhs_atom54(X20,X27,X28),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_120,plain,
! [X17,X10,X4] : lhs_atom44(X17,X10,X4),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_121,plain,
! [X2,X17,X4] : lhs_atom43(X2,X17,X4),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_122,plain,
! [X21,X22,X23] : lhs_atom37(X21,X22,X23),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_123,plain,
! [X21,X22,X23] : lhs_atom36(X21,X22,X23),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_124,plain,
! [X18,X3,X13] : lhs_atom33(X18,X3,X13),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_125,plain,
! [X17,X11,X4] : lhs_atom32(X17,X11,X4),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_126,plain,
! [X14,X15,X4] : lhs_atom30(X14,X15,X4),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_127,plain,
! [X1,X17,X4] : lhs_atom27(X1,X17,X4),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_128,plain,
! [X1,X17,X4] : lhs_atom26(X1,X17,X4),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_129,plain,
! [X12,X2,X4] : lhs_atom21(X12,X2,X4),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_130,plain,
! [X14,X15,X4] : lhs_atom20(X14,X15,X4),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_131,plain,
! [X2,X13,X4] : lhs_atom19(X2,X13,X4),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_132,plain,
! [X1,X2,X4] : lhs_atom18(X1,X2,X4),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_133,plain,
! [X1,X2,X4] : lhs_atom15(X1,X2,X4),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_134,plain,
! [X1,X2,X4] : lhs_atom6(X1,X2,X4),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_135,plain,
! [X2,X4] : lhs_atom94(X2,X4),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_136,plain,
! [X2,X33] : lhs_atom73(X2,X33),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_137,plain,
! [X18,X29] : lhs_atom69(X18,X29),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_138,plain,
! [X13,X32] : lhs_atom66(X13,X32),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_139,plain,
! [X13,X19] : lhs_atom65(X13,X19),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_140,plain,
! [X17,X4] : lhs_atom53(X17,X4),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_141,plain,
! [X20,X21] : lhs_atom42(X20,X21),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_142,plain,
! [X20,X21] : lhs_atom35(X20,X21),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_143,plain,
! [X19,X17] : lhs_atom34(X19,X17),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_144,plain,
! [X16,X4] : lhs_atom25(X16,X4),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_145,plain,
! [X1,X4] : lhs_atom9(X1,X4),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_146,plain,
! [X2,X4] : lhs_atom10(X2,X4),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_147,plain,
! [X1,X4] : lhs_atom9(X1,X4),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_148,plain,
! [X6,X4] : lhs_atom8(X6,X4),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_149,plain,
! [X6,X4] : lhs_atom8(X6,X4),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_150,plain,
! [X24] : lhs_atom62(X24),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_151,plain,
! [X17] : lhs_atom51(X17),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_152,plain,
! [X17] : lhs_atom49(X17),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_153,plain,
! [X24] : lhs_atom48(X24),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_154,plain,
! [X26] : lhs_atom47(X26),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_155,plain,
! [X26] : lhs_atom46(X26),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_156,plain,
! [X2] : lhs_atom40(X2),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_157,plain,
! [X24] : lhs_atom39(X24),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_158,plain,
! [X4] : lhs_atom29(X4),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_159,plain,
! [X4] : lhs_atom16(X4),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_160,plain,
! [X4] : lhs_atom5(X4),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_161,plain,
lhs_atom93,
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_162,plain,
lhs_atom92,
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_163,plain,
lhs_atom91,
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_164,plain,
lhs_atom90,
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_165,plain,
lhs_atom89,
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_166,plain,
lhs_atom88,
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_167,plain,
lhs_atom87,
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_168,plain,
lhs_atom86,
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_169,plain,
lhs_atom85,
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_170,plain,
lhs_atom84,
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_171,plain,
lhs_atom83,
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_172,plain,
lhs_atom82,
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_173,plain,
lhs_atom81,
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_174,plain,
lhs_atom80,
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_175,plain,
lhs_atom79,
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_176,plain,
lhs_atom78,
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_177,plain,
lhs_atom77,
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_178,plain,
lhs_atom76,
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_179,plain,
lhs_atom71,
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_180,plain,
lhs_atom67,
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_181,plain,
lhs_atom74,
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_182,plain,
lhs_atom72,
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_183,plain,
lhs_atom71,
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_184,plain,
lhs_atom70,
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_185,plain,
lhs_atom67,
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_186,plain,
lhs_atom60,
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_187,plain,
lhs_atom59,
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_188,plain,
lhs_atom58,
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_189,plain,
lhs_atom57,
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_190,plain,
lhs_atom56,
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_191,plain,
lhs_atom55,
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_192,plain,
lhs_atom50,
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_193,plain,
lhs_atom45,
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_194,plain,
lhs_atom38,
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_195,plain,
lhs_atom24,
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_196,plain,
! [X12,X13,X14,X15,X16,X17] : lhs_atom31(X12,X13,X14,X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_98]) ).
fof(c_0_197,plain,
! [X12,X13,X14,X15,X16,X17] : lhs_atom22(X12,X13,X14,X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_99]) ).
fof(c_0_198,plain,
! [X12,X13,X14,X15,X16,X17] : lhs_atom17(X12,X13,X14,X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_100]) ).
fof(c_0_199,plain,
! [X12,X13,X14,X15,X16,X17] : lhs_atom7(X12,X13,X14,X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_101]) ).
fof(c_0_200,plain,
! [X30,X31,X32,X33] : lhs_atom68(X30,X31,X32,X33),
inference(variable_rename,[status(thm)],[c_0_102]) ).
fof(c_0_201,plain,
! [X32,X33,X34,X35] : lhs_atom63(X32,X33,X34,X35),
inference(variable_rename,[status(thm)],[c_0_103]) ).
fof(c_0_202,plain,
! [X26,X27,X28,X29] : lhs_atom52(X26,X27,X28,X29),
inference(variable_rename,[status(thm)],[c_0_104]) ).
fof(c_0_203,plain,
! [X26,X27,X28,X29] : lhs_atom41(X26,X27,X28,X29),
inference(variable_rename,[status(thm)],[c_0_105]) ).
fof(c_0_204,plain,
! [X12,X13,X14,X15] : lhs_atom28(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_106]) ).
fof(c_0_205,plain,
! [X12,X13,X14,X15] : lhs_atom23(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_107]) ).
fof(c_0_206,plain,
! [X8,X9,X10,X11] : lhs_atom14(X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_108]) ).
fof(c_0_207,plain,
! [X13,X14,X15,X16] : lhs_atom13(X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_109]) ).
fof(c_0_208,plain,
! [X7,X8,X9,X10] : lhs_atom12(X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_110]) ).
fof(c_0_209,plain,
! [X13,X14,X15,X16] : lhs_atom11(X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_111]) ).
fof(c_0_210,plain,
! [X7,X8,X9,X10] : lhs_atom4(X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_112]) ).
fof(c_0_211,plain,
! [X9,X10,X11,X12] : lhs_atom3(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_113]) ).
fof(c_0_212,plain,
! [X7,X8,X9,X10] : lhs_atom2(X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_114]) ).
fof(c_0_213,plain,
! [X5,X6,X7,X8] : lhs_atom1(X5,X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_115]) ).
fof(c_0_214,plain,
! [X30,X31,X32] : lhs_atom75(X30,X31,X32),
inference(variable_rename,[status(thm)],[c_0_116]) ).
fof(c_0_215,plain,
! [X29,X30,X31] : lhs_atom64(X29,X30,X31),
inference(variable_rename,[status(thm)],[c_0_117]) ).
fof(c_0_216,plain,
! [X30,X31,X32] : lhs_atom61(X30,X31,X32),
inference(variable_rename,[status(thm)],[c_0_118]) ).
fof(c_0_217,plain,
! [X29,X30,X31] : lhs_atom54(X29,X30,X31),
inference(variable_rename,[status(thm)],[c_0_119]) ).
fof(c_0_218,plain,
! [X18,X19,X20] : lhs_atom44(X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_120]) ).
fof(c_0_219,plain,
! [X18,X19,X20] : lhs_atom43(X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_121]) ).
fof(c_0_220,plain,
! [X24,X25,X26] : lhs_atom37(X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_122]) ).
fof(c_0_221,plain,
! [X24,X25,X26] : lhs_atom36(X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_123]) ).
fof(c_0_222,plain,
! [X19,X20,X21] : lhs_atom33(X19,X20,X21),
inference(variable_rename,[status(thm)],[c_0_124]) ).
fof(c_0_223,plain,
! [X18,X19,X20] : lhs_atom32(X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_125]) ).
fof(c_0_224,plain,
! [X16,X17,X18] : lhs_atom30(X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_126]) ).
fof(c_0_225,plain,
! [X18,X19,X20] : lhs_atom27(X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_127]) ).
fof(c_0_226,plain,
! [X18,X19,X20] : lhs_atom26(X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_128]) ).
fof(c_0_227,plain,
! [X13,X14,X15] : lhs_atom21(X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_129]) ).
fof(c_0_228,plain,
! [X16,X17,X18] : lhs_atom20(X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_130]) ).
fof(c_0_229,plain,
! [X14,X15,X16] : lhs_atom19(X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_131]) ).
fof(c_0_230,plain,
! [X5,X6,X7] : lhs_atom18(X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_132]) ).
fof(c_0_231,plain,
! [X5,X6,X7] : lhs_atom15(X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_133]) ).
fof(c_0_232,plain,
! [X5,X6,X7] : lhs_atom6(X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_134]) ).
fof(c_0_233,plain,
! [X5,X6] : lhs_atom94(X5,X6),
inference(variable_rename,[status(thm)],[c_0_135]) ).
fof(c_0_234,plain,
! [X34,X35] : lhs_atom73(X34,X35),
inference(variable_rename,[status(thm)],[c_0_136]) ).
fof(c_0_235,plain,
! [X30,X31] : lhs_atom69(X30,X31),
inference(variable_rename,[status(thm)],[c_0_137]) ).
fof(c_0_236,plain,
! [X33,X34] : lhs_atom66(X33,X34),
inference(variable_rename,[status(thm)],[c_0_138]) ).
fof(c_0_237,plain,
! [X20,X21] : lhs_atom65(X20,X21),
inference(variable_rename,[status(thm)],[c_0_139]) ).
fof(c_0_238,plain,
! [X18,X19] : lhs_atom53(X18,X19),
inference(variable_rename,[status(thm)],[c_0_140]) ).
fof(c_0_239,plain,
! [X22,X23] : lhs_atom42(X22,X23),
inference(variable_rename,[status(thm)],[c_0_141]) ).
fof(c_0_240,plain,
! [X22,X23] : lhs_atom35(X22,X23),
inference(variable_rename,[status(thm)],[c_0_142]) ).
fof(c_0_241,plain,
! [X20,X21] : lhs_atom34(X20,X21),
inference(variable_rename,[status(thm)],[c_0_143]) ).
fof(c_0_242,plain,
! [X17,X18] : lhs_atom25(X17,X18),
inference(variable_rename,[status(thm)],[c_0_144]) ).
fof(c_0_243,plain,
! [X5,X6] : lhs_atom9(X5,X6),
inference(variable_rename,[status(thm)],[c_0_145]) ).
fof(c_0_244,plain,
! [X5,X6] : lhs_atom10(X5,X6),
inference(variable_rename,[status(thm)],[c_0_146]) ).
fof(c_0_245,plain,
! [X5,X6] : lhs_atom9(X5,X6),
inference(variable_rename,[status(thm)],[c_0_147]) ).
fof(c_0_246,plain,
! [X7,X8] : lhs_atom8(X7,X8),
inference(variable_rename,[status(thm)],[c_0_148]) ).
fof(c_0_247,plain,
! [X7,X8] : lhs_atom8(X7,X8),
inference(variable_rename,[status(thm)],[c_0_149]) ).
fof(c_0_248,plain,
! [X25] : lhs_atom62(X25),
inference(variable_rename,[status(thm)],[c_0_150]) ).
fof(c_0_249,plain,
! [X18] : lhs_atom51(X18),
inference(variable_rename,[status(thm)],[c_0_151]) ).
fof(c_0_250,plain,
! [X18] : lhs_atom49(X18),
inference(variable_rename,[status(thm)],[c_0_152]) ).
fof(c_0_251,plain,
! [X25] : lhs_atom48(X25),
inference(variable_rename,[status(thm)],[c_0_153]) ).
fof(c_0_252,plain,
! [X27] : lhs_atom47(X27),
inference(variable_rename,[status(thm)],[c_0_154]) ).
fof(c_0_253,plain,
! [X27] : lhs_atom46(X27),
inference(variable_rename,[status(thm)],[c_0_155]) ).
fof(c_0_254,plain,
! [X3] : lhs_atom40(X3),
inference(variable_rename,[status(thm)],[c_0_156]) ).
fof(c_0_255,plain,
! [X25] : lhs_atom39(X25),
inference(variable_rename,[status(thm)],[c_0_157]) ).
fof(c_0_256,plain,
! [X5] : lhs_atom29(X5),
inference(variable_rename,[status(thm)],[c_0_158]) ).
fof(c_0_257,plain,
! [X5] : lhs_atom16(X5),
inference(variable_rename,[status(thm)],[c_0_159]) ).
fof(c_0_258,plain,
! [X5] : lhs_atom5(X5),
inference(variable_rename,[status(thm)],[c_0_160]) ).
fof(c_0_259,plain,
lhs_atom93,
c_0_161 ).
fof(c_0_260,plain,
lhs_atom92,
c_0_162 ).
fof(c_0_261,plain,
lhs_atom91,
c_0_163 ).
fof(c_0_262,plain,
lhs_atom90,
c_0_164 ).
fof(c_0_263,plain,
lhs_atom89,
c_0_165 ).
fof(c_0_264,plain,
lhs_atom88,
c_0_166 ).
fof(c_0_265,plain,
lhs_atom87,
c_0_167 ).
fof(c_0_266,plain,
lhs_atom86,
c_0_168 ).
fof(c_0_267,plain,
lhs_atom85,
c_0_169 ).
fof(c_0_268,plain,
lhs_atom84,
c_0_170 ).
fof(c_0_269,plain,
lhs_atom83,
c_0_171 ).
fof(c_0_270,plain,
lhs_atom82,
c_0_172 ).
fof(c_0_271,plain,
lhs_atom81,
c_0_173 ).
fof(c_0_272,plain,
lhs_atom80,
c_0_174 ).
fof(c_0_273,plain,
lhs_atom79,
c_0_175 ).
fof(c_0_274,plain,
lhs_atom78,
c_0_176 ).
fof(c_0_275,plain,
lhs_atom77,
c_0_177 ).
fof(c_0_276,plain,
lhs_atom76,
c_0_178 ).
fof(c_0_277,plain,
lhs_atom71,
c_0_179 ).
fof(c_0_278,plain,
lhs_atom67,
c_0_180 ).
fof(c_0_279,plain,
lhs_atom74,
c_0_181 ).
fof(c_0_280,plain,
lhs_atom72,
c_0_182 ).
fof(c_0_281,plain,
lhs_atom71,
c_0_183 ).
fof(c_0_282,plain,
lhs_atom70,
c_0_184 ).
fof(c_0_283,plain,
lhs_atom67,
c_0_185 ).
fof(c_0_284,plain,
lhs_atom60,
c_0_186 ).
fof(c_0_285,plain,
lhs_atom59,
c_0_187 ).
fof(c_0_286,plain,
lhs_atom58,
c_0_188 ).
fof(c_0_287,plain,
lhs_atom57,
c_0_189 ).
fof(c_0_288,plain,
lhs_atom56,
c_0_190 ).
fof(c_0_289,plain,
lhs_atom55,
c_0_191 ).
fof(c_0_290,plain,
lhs_atom50,
c_0_192 ).
fof(c_0_291,plain,
lhs_atom45,
c_0_193 ).
fof(c_0_292,plain,
lhs_atom38,
c_0_194 ).
fof(c_0_293,plain,
lhs_atom24,
c_0_195 ).
cnf(c_0_294,plain,
lhs_atom31(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_196]) ).
cnf(c_0_295,plain,
lhs_atom22(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_197]) ).
cnf(c_0_296,plain,
lhs_atom17(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_198]) ).
cnf(c_0_297,plain,
lhs_atom7(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_199]) ).
cnf(c_0_298,plain,
lhs_atom68(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_200]) ).
cnf(c_0_299,plain,
lhs_atom63(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_201]) ).
cnf(c_0_300,plain,
lhs_atom52(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_202]) ).
cnf(c_0_301,plain,
lhs_atom41(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_203]) ).
cnf(c_0_302,plain,
lhs_atom28(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_204]) ).
cnf(c_0_303,plain,
lhs_atom23(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_205]) ).
cnf(c_0_304,plain,
lhs_atom14(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_206]) ).
cnf(c_0_305,plain,
lhs_atom13(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_207]) ).
cnf(c_0_306,plain,
lhs_atom12(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_208]) ).
cnf(c_0_307,plain,
lhs_atom11(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_209]) ).
cnf(c_0_308,plain,
lhs_atom4(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_210]) ).
cnf(c_0_309,plain,
lhs_atom3(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_211]) ).
cnf(c_0_310,plain,
lhs_atom2(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_212]) ).
cnf(c_0_311,plain,
lhs_atom1(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_312,plain,
lhs_atom75(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_214]) ).
cnf(c_0_313,plain,
lhs_atom64(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_215]) ).
cnf(c_0_314,plain,
lhs_atom61(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_216]) ).
cnf(c_0_315,plain,
lhs_atom54(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_217]) ).
cnf(c_0_316,plain,
lhs_atom44(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_218]) ).
cnf(c_0_317,plain,
lhs_atom43(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_219]) ).
cnf(c_0_318,plain,
lhs_atom37(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_220]) ).
cnf(c_0_319,plain,
lhs_atom36(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_221]) ).
cnf(c_0_320,plain,
lhs_atom33(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_222]) ).
cnf(c_0_321,plain,
lhs_atom32(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_223]) ).
cnf(c_0_322,plain,
lhs_atom30(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_224]) ).
cnf(c_0_323,plain,
lhs_atom27(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_225]) ).
cnf(c_0_324,plain,
lhs_atom26(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_325,plain,
lhs_atom21(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_326,plain,
lhs_atom20(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_327,plain,
lhs_atom19(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_328,plain,
lhs_atom18(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_329,plain,
lhs_atom15(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_330,plain,
lhs_atom6(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_331,plain,
lhs_atom94(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_332,plain,
lhs_atom73(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_333,plain,
lhs_atom69(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_235]) ).
cnf(c_0_334,plain,
lhs_atom66(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_335,plain,
lhs_atom65(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_336,plain,
lhs_atom53(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_337,plain,
lhs_atom42(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_338,plain,
lhs_atom35(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_339,plain,
lhs_atom34(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
cnf(c_0_340,plain,
lhs_atom25(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_341,plain,
lhs_atom9(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_243]) ).
cnf(c_0_342,plain,
lhs_atom10(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_343,plain,
lhs_atom9(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_245]) ).
cnf(c_0_344,plain,
lhs_atom8(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_345,plain,
lhs_atom8(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_247]) ).
cnf(c_0_346,plain,
lhs_atom62(X1),
inference(split_conjunct,[status(thm)],[c_0_248]) ).
cnf(c_0_347,plain,
lhs_atom51(X1),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
cnf(c_0_348,plain,
lhs_atom49(X1),
inference(split_conjunct,[status(thm)],[c_0_250]) ).
cnf(c_0_349,plain,
lhs_atom48(X1),
inference(split_conjunct,[status(thm)],[c_0_251]) ).
cnf(c_0_350,plain,
lhs_atom47(X1),
inference(split_conjunct,[status(thm)],[c_0_252]) ).
cnf(c_0_351,plain,
lhs_atom46(X1),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
cnf(c_0_352,plain,
lhs_atom40(X1),
inference(split_conjunct,[status(thm)],[c_0_254]) ).
cnf(c_0_353,plain,
lhs_atom39(X1),
inference(split_conjunct,[status(thm)],[c_0_255]) ).
cnf(c_0_354,plain,
lhs_atom29(X1),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_355,plain,
lhs_atom16(X1),
inference(split_conjunct,[status(thm)],[c_0_257]) ).
cnf(c_0_356,plain,
lhs_atom5(X1),
inference(split_conjunct,[status(thm)],[c_0_258]) ).
cnf(c_0_357,plain,
lhs_atom93,
inference(split_conjunct,[status(thm)],[c_0_259]) ).
cnf(c_0_358,plain,
lhs_atom92,
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_359,plain,
lhs_atom91,
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_360,plain,
lhs_atom90,
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_361,plain,
lhs_atom89,
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_362,plain,
lhs_atom88,
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_363,plain,
lhs_atom87,
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_364,plain,
lhs_atom86,
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_365,plain,
lhs_atom85,
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_366,plain,
lhs_atom84,
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_367,plain,
lhs_atom83,
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_368,plain,
lhs_atom82,
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_369,plain,
lhs_atom81,
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_370,plain,
lhs_atom80,
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_371,plain,
lhs_atom79,
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_372,plain,
lhs_atom78,
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_373,plain,
lhs_atom77,
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_374,plain,
lhs_atom76,
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_375,plain,
lhs_atom71,
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_376,plain,
lhs_atom67,
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_377,plain,
lhs_atom74,
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_378,plain,
lhs_atom72,
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_379,plain,
lhs_atom71,
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_380,plain,
lhs_atom70,
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_381,plain,
lhs_atom67,
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_382,plain,
lhs_atom60,
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_383,plain,
lhs_atom59,
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_384,plain,
lhs_atom58,
inference(split_conjunct,[status(thm)],[c_0_286]) ).
cnf(c_0_385,plain,
lhs_atom57,
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_386,plain,
lhs_atom56,
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_387,plain,
lhs_atom55,
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_388,plain,
lhs_atom50,
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_389,plain,
lhs_atom45,
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_390,plain,
lhs_atom38,
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_391,plain,
lhs_atom24,
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_392,plain,
lhs_atom31(X1,X2,X3,X4,X5,X6),
c_0_294,
[final] ).
cnf(c_0_393,plain,
lhs_atom22(X1,X2,X3,X4,X5,X6),
c_0_295,
[final] ).
cnf(c_0_394,plain,
lhs_atom17(X1,X2,X3,X4,X5,X6),
c_0_296,
[final] ).
cnf(c_0_395,plain,
lhs_atom7(X1,X2,X3,X4,X5,X6),
c_0_297,
[final] ).
cnf(c_0_396,plain,
lhs_atom68(X1,X2,X3,X4),
c_0_298,
[final] ).
cnf(c_0_397,plain,
lhs_atom63(X1,X2,X3,X4),
c_0_299,
[final] ).
cnf(c_0_398,plain,
lhs_atom52(X1,X2,X3,X4),
c_0_300,
[final] ).
cnf(c_0_399,plain,
lhs_atom41(X1,X2,X3,X4),
c_0_301,
[final] ).
cnf(c_0_400,plain,
lhs_atom28(X1,X2,X3,X4),
c_0_302,
[final] ).
cnf(c_0_401,plain,
lhs_atom23(X1,X2,X3,X4),
c_0_303,
[final] ).
cnf(c_0_402,plain,
lhs_atom14(X1,X2,X3,X4),
c_0_304,
[final] ).
cnf(c_0_403,plain,
lhs_atom13(X1,X2,X3,X4),
c_0_305,
[final] ).
cnf(c_0_404,plain,
lhs_atom12(X1,X2,X3,X4),
c_0_306,
[final] ).
cnf(c_0_405,plain,
lhs_atom11(X1,X2,X3,X4),
c_0_307,
[final] ).
cnf(c_0_406,plain,
lhs_atom4(X1,X2,X3,X4),
c_0_308,
[final] ).
cnf(c_0_407,plain,
lhs_atom3(X1,X2,X3,X4),
c_0_309,
[final] ).
cnf(c_0_408,plain,
lhs_atom2(X1,X2,X3,X4),
c_0_310,
[final] ).
cnf(c_0_409,plain,
lhs_atom1(X1,X2,X3,X4),
c_0_311,
[final] ).
cnf(c_0_410,plain,
lhs_atom75(X1,X2,X3),
c_0_312,
[final] ).
cnf(c_0_411,plain,
lhs_atom64(X1,X2,X3),
c_0_313,
[final] ).
cnf(c_0_412,plain,
lhs_atom61(X1,X2,X3),
c_0_314,
[final] ).
cnf(c_0_413,plain,
lhs_atom54(X1,X2,X3),
c_0_315,
[final] ).
cnf(c_0_414,plain,
lhs_atom44(X1,X2,X3),
c_0_316,
[final] ).
cnf(c_0_415,plain,
lhs_atom43(X1,X2,X3),
c_0_317,
[final] ).
cnf(c_0_416,plain,
lhs_atom37(X1,X2,X3),
c_0_318,
[final] ).
cnf(c_0_417,plain,
lhs_atom36(X1,X2,X3),
c_0_319,
[final] ).
cnf(c_0_418,plain,
lhs_atom33(X1,X2,X3),
c_0_320,
[final] ).
cnf(c_0_419,plain,
lhs_atom32(X1,X2,X3),
c_0_321,
[final] ).
cnf(c_0_420,plain,
lhs_atom30(X1,X2,X3),
c_0_322,
[final] ).
cnf(c_0_421,plain,
lhs_atom27(X1,X2,X3),
c_0_323,
[final] ).
cnf(c_0_422,plain,
lhs_atom26(X1,X2,X3),
c_0_324,
[final] ).
cnf(c_0_423,plain,
lhs_atom21(X1,X2,X3),
c_0_325,
[final] ).
cnf(c_0_424,plain,
lhs_atom20(X1,X2,X3),
c_0_326,
[final] ).
cnf(c_0_425,plain,
lhs_atom19(X1,X2,X3),
c_0_327,
[final] ).
cnf(c_0_426,plain,
lhs_atom18(X1,X2,X3),
c_0_328,
[final] ).
cnf(c_0_427,plain,
lhs_atom15(X1,X2,X3),
c_0_329,
[final] ).
cnf(c_0_428,plain,
lhs_atom6(X1,X2,X3),
c_0_330,
[final] ).
cnf(c_0_429,plain,
lhs_atom94(X1,X2),
c_0_331,
[final] ).
cnf(c_0_430,plain,
lhs_atom73(X1,X2),
c_0_332,
[final] ).
cnf(c_0_431,plain,
lhs_atom69(X1,X2),
c_0_333,
[final] ).
cnf(c_0_432,plain,
lhs_atom66(X1,X2),
c_0_334,
[final] ).
cnf(c_0_433,plain,
lhs_atom65(X1,X2),
c_0_335,
[final] ).
cnf(c_0_434,plain,
lhs_atom53(X1,X2),
c_0_336,
[final] ).
cnf(c_0_435,plain,
lhs_atom42(X1,X2),
c_0_337,
[final] ).
cnf(c_0_436,plain,
lhs_atom35(X1,X2),
c_0_338,
[final] ).
cnf(c_0_437,plain,
lhs_atom34(X1,X2),
c_0_339,
[final] ).
cnf(c_0_438,plain,
lhs_atom25(X1,X2),
c_0_340,
[final] ).
cnf(c_0_439,plain,
lhs_atom9(X1,X2),
c_0_341,
[final] ).
cnf(c_0_440,plain,
lhs_atom10(X1,X2),
c_0_342,
[final] ).
cnf(c_0_441,plain,
lhs_atom9(X1,X2),
c_0_343,
[final] ).
cnf(c_0_442,plain,
lhs_atom8(X1,X2),
c_0_344,
[final] ).
cnf(c_0_443,plain,
lhs_atom8(X1,X2),
c_0_345,
[final] ).
cnf(c_0_444,plain,
lhs_atom62(X1),
c_0_346,
[final] ).
cnf(c_0_445,plain,
lhs_atom51(X1),
c_0_347,
[final] ).
cnf(c_0_446,plain,
lhs_atom49(X1),
c_0_348,
[final] ).
cnf(c_0_447,plain,
lhs_atom48(X1),
c_0_349,
[final] ).
cnf(c_0_448,plain,
lhs_atom47(X1),
c_0_350,
[final] ).
cnf(c_0_449,plain,
lhs_atom46(X1),
c_0_351,
[final] ).
cnf(c_0_450,plain,
lhs_atom40(X1),
c_0_352,
[final] ).
cnf(c_0_451,plain,
lhs_atom39(X1),
c_0_353,
[final] ).
cnf(c_0_452,plain,
lhs_atom29(X1),
c_0_354,
[final] ).
cnf(c_0_453,plain,
lhs_atom16(X1),
c_0_355,
[final] ).
cnf(c_0_454,plain,
lhs_atom5(X1),
c_0_356,
[final] ).
cnf(c_0_455,plain,
lhs_atom93,
c_0_357,
[final] ).
cnf(c_0_456,plain,
lhs_atom92,
c_0_358,
[final] ).
cnf(c_0_457,plain,
lhs_atom91,
c_0_359,
[final] ).
cnf(c_0_458,plain,
lhs_atom90,
c_0_360,
[final] ).
cnf(c_0_459,plain,
lhs_atom89,
c_0_361,
[final] ).
cnf(c_0_460,plain,
lhs_atom88,
c_0_362,
[final] ).
cnf(c_0_461,plain,
lhs_atom87,
c_0_363,
[final] ).
cnf(c_0_462,plain,
lhs_atom86,
c_0_364,
[final] ).
cnf(c_0_463,plain,
lhs_atom85,
c_0_365,
[final] ).
cnf(c_0_464,plain,
lhs_atom84,
c_0_366,
[final] ).
cnf(c_0_465,plain,
lhs_atom83,
c_0_367,
[final] ).
cnf(c_0_466,plain,
lhs_atom82,
c_0_368,
[final] ).
cnf(c_0_467,plain,
lhs_atom81,
c_0_369,
[final] ).
cnf(c_0_468,plain,
lhs_atom80,
c_0_370,
[final] ).
cnf(c_0_469,plain,
lhs_atom79,
c_0_371,
[final] ).
cnf(c_0_470,plain,
lhs_atom78,
c_0_372,
[final] ).
cnf(c_0_471,plain,
lhs_atom77,
c_0_373,
[final] ).
cnf(c_0_472,plain,
lhs_atom76,
c_0_374,
[final] ).
cnf(c_0_473,plain,
lhs_atom71,
c_0_375,
[final] ).
cnf(c_0_474,plain,
lhs_atom67,
c_0_376,
[final] ).
cnf(c_0_475,plain,
lhs_atom74,
c_0_377,
[final] ).
cnf(c_0_476,plain,
lhs_atom72,
c_0_378,
[final] ).
cnf(c_0_477,plain,
lhs_atom71,
c_0_379,
[final] ).
cnf(c_0_478,plain,
lhs_atom70,
c_0_380,
[final] ).
cnf(c_0_479,plain,
lhs_atom67,
c_0_381,
[final] ).
cnf(c_0_480,plain,
lhs_atom60,
c_0_382,
[final] ).
cnf(c_0_481,plain,
lhs_atom59,
c_0_383,
[final] ).
cnf(c_0_482,plain,
lhs_atom58,
c_0_384,
[final] ).
cnf(c_0_483,plain,
lhs_atom57,
c_0_385,
[final] ).
cnf(c_0_484,plain,
lhs_atom56,
c_0_386,
[final] ).
cnf(c_0_485,plain,
lhs_atom55,
c_0_387,
[final] ).
cnf(c_0_486,plain,
lhs_atom50,
c_0_388,
[final] ).
cnf(c_0_487,plain,
lhs_atom45,
c_0_389,
[final] ).
cnf(c_0_488,plain,
lhs_atom38,
c_0_390,
[final] ).
cnf(c_0_489,plain,
lhs_atom24,
c_0_391,
[final] ).
% End CNF derivation
cnf(c_0_392_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_392,def_lhs_atom31]) ).
cnf(c_0_393_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_393,def_lhs_atom22]) ).
cnf(c_0_394_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_394,def_lhs_atom17]) ).
cnf(c_0_395_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_395,def_lhs_atom7]) ).
cnf(c_0_396_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_396,def_lhs_atom68]) ).
cnf(c_0_397_0,axiom,
hAPP(c_Type_Oshift(X2,X1,X3,X4),X1) = X3,
inference(unfold_definition,[status(thm)],[c_0_397,def_lhs_atom63]) ).
cnf(c_0_398_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_398,def_lhs_atom52]) ).
cnf(c_0_399_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_399,def_lhs_atom41]) ).
cnf(c_0_400_0,axiom,
c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3) = X2,
inference(unfold_definition,[status(thm)],[c_0_400,def_lhs_atom28]) ).
cnf(c_0_401_0,axiom,
c_List_Ofoldr(X1,c_List_Olist_ONil(X3),X2,X3,X4) = X2,
inference(unfold_definition,[status(thm)],[c_0_401,def_lhs_atom23]) ).
cnf(c_0_402_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_402,def_lhs_atom14]) ).
cnf(c_0_403_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_403,def_lhs_atom13]) ).
cnf(c_0_404_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_404,def_lhs_atom12]) ).
cnf(c_0_405_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_405,def_lhs_atom11]) ).
cnf(c_0_406_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_406,def_lhs_atom4]) ).
cnf(c_0_407_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_407,def_lhs_atom3]) ).
cnf(c_0_408_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_408,def_lhs_atom2]) ).
cnf(c_0_409_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_409,def_lhs_atom1]) ).
cnf(c_0_410_0,axiom,
c_Lambda_Osubst(c_Lambda_Olift(X1,X3),X2,X3) = X1,
inference(unfold_definition,[status(thm)],[c_0_410,def_lhs_atom75]) ).
cnf(c_0_411_0,axiom,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2),
inference(unfold_definition,[status(thm)],[c_0_411,def_lhs_atom64]) ).
cnf(c_0_412_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_412,def_lhs_atom61]) ).
cnf(c_0_413_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2) != c_Lambda_OdB_OVar(X1),
inference(unfold_definition,[status(thm)],[c_0_413,def_lhs_atom54]) ).
cnf(c_0_414_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X3),X2),X2)),
inference(unfold_definition,[status(thm)],[c_0_414,def_lhs_atom44]) ).
cnf(c_0_415_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X2,X3),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_415,def_lhs_atom43]) ).
cnf(c_0_416_0,axiom,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2),
inference(unfold_definition,[status(thm)],[c_0_416,def_lhs_atom37]) ).
cnf(c_0_417_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2) != c_Lambda_OdB_OAbs(X1),
inference(unfold_definition,[status(thm)],[c_0_417,def_lhs_atom36]) ).
cnf(c_0_418_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_418,def_lhs_atom33]) ).
cnf(c_0_419_0,axiom,
c_Predicate_Oconversep(c_Predicate_Oconversep(X1,X3,X2),X2,X3) = X1,
inference(unfold_definition,[status(thm)],[c_0_419,def_lhs_atom32]) ).
cnf(c_0_420_0,axiom,
c_List_Olist_ONil(X3) != c_List_Olist_OCons(X2,X1,X3),
inference(unfold_definition,[status(thm)],[c_0_420,def_lhs_atom30]) ).
cnf(c_0_421_0,axiom,
~ c_ListOrder_Ostep1(X2,X1,c_List_Olist_ONil(X3),X3),
inference(unfold_definition,[status(thm)],[c_0_421,def_lhs_atom27]) ).
cnf(c_0_422_0,axiom,
~ c_ListOrder_Ostep1(X2,c_List_Olist_ONil(X3),X1,X3),
inference(unfold_definition,[status(thm)],[c_0_422,def_lhs_atom26]) ).
cnf(c_0_423_0,axiom,
c_List_Olist_OCons(X2,X1,X3) != c_List_Olist_ONil(X3),
inference(unfold_definition,[status(thm)],[c_0_423,def_lhs_atom21]) ).
cnf(c_0_424_0,axiom,
c_List_Olist_OCons(X2,X1,X3) != c_List_Olist_ONil(X3),
inference(unfold_definition,[status(thm)],[c_0_424,def_lhs_atom20]) ).
cnf(c_0_425_0,axiom,
c_List_Olist_OCons(X1,X2,X3) != X2,
inference(unfold_definition,[status(thm)],[c_0_425,def_lhs_atom19]) ).
cnf(c_0_426_0,axiom,
X1 != c_List_Olist_OCons(X2,X1,X3),
inference(unfold_definition,[status(thm)],[c_0_426,def_lhs_atom18]) ).
cnf(c_0_427_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_427,def_lhs_atom15]) ).
cnf(c_0_428_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_428,def_lhs_atom6]) ).
cnf(c_0_429_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X2),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_429,def_lhs_atom94]) ).
cnf(c_0_430_0,axiom,
c_Type_Otyping(X2,c_Lambda_OdB_OVar(X1),hAPP(X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_430,def_lhs_atom73]) ).
cnf(c_0_431_0,axiom,
c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_431,def_lhs_atom69]) ).
cnf(c_0_432_0,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X2)),X1)),
inference(unfold_definition,[status(thm)],[c_0_432,def_lhs_atom66]) ).
cnf(c_0_433_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_433,def_lhs_atom65]) ).
cnf(c_0_434_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_434,def_lhs_atom53]) ).
cnf(c_0_435_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
inference(unfold_definition,[status(thm)],[c_0_435,def_lhs_atom42]) ).
cnf(c_0_436_0,axiom,
c_Lambda_OdB_OAbs(X2) != c_Lambda_OdB_OVar(X1),
inference(unfold_definition,[status(thm)],[c_0_436,def_lhs_atom35]) ).
cnf(c_0_437_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_437,def_lhs_atom34]) ).
cnf(c_0_438_0,axiom,
c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2),
inference(unfold_definition,[status(thm)],[c_0_438,def_lhs_atom25]) ).
cnf(c_0_439_0,axiom,
c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_439,def_lhs_atom9]) ).
cnf(c_0_440_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_440,def_lhs_atom10]) ).
cnf(c_0_441_0,axiom,
c_List_Oappend(X1,c_List_Olist_ONil(X2),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_441,def_lhs_atom9]) ).
cnf(c_0_442_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_442,def_lhs_atom8]) ).
cnf(c_0_443_0,axiom,
c_List_Oappend(c_List_Olist_ONil(X2),X1,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_443,def_lhs_atom8]) ).
cnf(c_0_444_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
inference(unfold_definition,[status(thm)],[c_0_444,def_lhs_atom62]) ).
cnf(c_0_445_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_445,def_lhs_atom51]) ).
cnf(c_0_446_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_446,def_lhs_atom49]) ).
cnf(c_0_447_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_447,def_lhs_atom48]) ).
cnf(c_0_448_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(unfold_definition,[status(thm)],[c_0_448,def_lhs_atom47]) ).
cnf(c_0_449_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_449,def_lhs_atom46]) ).
cnf(c_0_450_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_450,def_lhs_atom40]) ).
cnf(c_0_451_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
inference(unfold_definition,[status(thm)],[c_0_451,def_lhs_atom39]) ).
cnf(c_0_452_0,axiom,
c_Predicate_Oconversep(c_fequal(X1),X1,X1) = c_fequal(X1),
inference(unfold_definition,[status(thm)],[c_0_452,def_lhs_atom29]) ).
cnf(c_0_453_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_453,def_lhs_atom16]) ).
cnf(c_0_454_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_454,def_lhs_atom5]) ).
cnf(c_0_455_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_455,def_lhs_atom93]) ).
cnf(c_0_456_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_456,def_lhs_atom92]) ).
cnf(c_0_457_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_457,def_lhs_atom91]) ).
cnf(c_0_458_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_458,def_lhs_atom90]) ).
cnf(c_0_459_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_459,def_lhs_atom89]) ).
cnf(c_0_460_0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_460,def_lhs_atom88]) ).
cnf(c_0_461_0,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_461,def_lhs_atom87]) ).
cnf(c_0_462_0,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_462,def_lhs_atom86]) ).
cnf(c_0_463_0,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_463,def_lhs_atom85]) ).
cnf(c_0_464_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_464,def_lhs_atom84]) ).
cnf(c_0_465_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_465,def_lhs_atom83]) ).
cnf(c_0_466_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_466,def_lhs_atom82]) ).
cnf(c_0_467_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_467,def_lhs_atom81]) ).
cnf(c_0_468_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_468,def_lhs_atom80]) ).
cnf(c_0_469_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_469,def_lhs_atom79]) ).
cnf(c_0_470_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_470,def_lhs_atom78]) ).
cnf(c_0_471_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_471,def_lhs_atom77]) ).
cnf(c_0_472_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_472,def_lhs_atom76]) ).
cnf(c_0_473_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
inference(unfold_definition,[status(thm)],[c_0_473,def_lhs_atom71]) ).
cnf(c_0_474_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(unfold_definition,[status(thm)],[c_0_474,def_lhs_atom67]) ).
cnf(c_0_475_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(unfold_definition,[status(thm)],[c_0_475,def_lhs_atom74]) ).
cnf(c_0_476_0,axiom,
v_n____ = v_i____,
inference(unfold_definition,[status(thm)],[c_0_476,def_lhs_atom72]) ).
cnf(c_0_477_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
inference(unfold_definition,[status(thm)],[c_0_477,def_lhs_atom71]) ).
cnf(c_0_478_0,axiom,
c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(unfold_definition,[status(thm)],[c_0_478,def_lhs_atom70]) ).
cnf(c_0_479_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(unfold_definition,[status(thm)],[c_0_479,def_lhs_atom67]) ).
cnf(c_0_480_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______),
inference(unfold_definition,[status(thm)],[c_0_480,def_lhs_atom60]) ).
cnf(c_0_481_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(unfold_definition,[status(thm)],[c_0_481,def_lhs_atom59]) ).
cnf(c_0_482_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(unfold_definition,[status(thm)],[c_0_482,def_lhs_atom58]) ).
cnf(c_0_483_0,axiom,
c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
inference(unfold_definition,[status(thm)],[c_0_483,def_lhs_atom57]) ).
cnf(c_0_484_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(unfold_definition,[status(thm)],[c_0_484,def_lhs_atom56]) ).
cnf(c_0_485_0,axiom,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(unfold_definition,[status(thm)],[c_0_485,def_lhs_atom55]) ).
cnf(c_0_486_0,axiom,
v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),
inference(unfold_definition,[status(thm)],[c_0_486,def_lhs_atom50]) ).
cnf(c_0_487_0,axiom,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
inference(unfold_definition,[status(thm)],[c_0_487,def_lhs_atom45]) ).
cnf(c_0_488_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_488,def_lhs_atom38]) ).
cnf(c_0_489_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
inference(unfold_definition,[status(thm)],[c_0_489,def_lhs_atom24]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X27,X28,X8,X14,X10,X29,X11] :
( X10 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X11,X10,X14,X27),X11,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X10)
| ~ c_Type_Otypings(X14,X28,X29)
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X27,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
file('<stdin>',cls_var__app__types_0) ).
fof(c_0_1_002,axiom,
! [X39,X19,X20] :
( X39 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X20,X19,X39),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X19,tc_Lambda_OdB,tc_Lambda_OdB)),X39)) ),
file('<stdin>',cls_head__Var__reduction_1) ).
fof(c_0_2_003,axiom,
! [X27,X28,X8,X14,X10,X29,X11] :
( c_Type_Otypings(X14,X27,c_Type_Osko__Type__Xvar__app__types__1__1(X11,X10,X14,X27))
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X10)
| ~ c_Type_Otypings(X14,X28,X29)
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X27,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
file('<stdin>',cls_var__app__types_1) ).
fof(c_0_3_004,axiom,
! [X39,X19,X20] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X19,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X20,X19,X39),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X19,tc_Lambda_OdB,tc_Lambda_OdB)),X39)) ),
file('<stdin>',cls_head__Var__reduction_0) ).
fof(c_0_4_005,axiom,
! [X18,X19,X13] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X13,X19,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X13,X18,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X19,X18,tc_Lambda_OdB) ),
file('<stdin>',cls_apps__preserves__betas_0) ).
fof(c_0_5_006,axiom,
! [X18,X12,X13] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X13,X18,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X13),X12)) ),
file('<stdin>',cls_apps__preserves__beta2_0) ).
fof(c_0_6_007,axiom,
! [X18,X12,X13] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X13,X18,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X13),X12)) ),
file('<stdin>',cls_apps__preserves__beta_0) ).
fof(c_0_7_008,axiom,
! [X18,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),X18,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)),X18,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('<stdin>',cls_Beta_0) ).
fof(c_0_8_009,axiom,
! [X28,X8,X14,X10,X11] :
( X11 = X10
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X10)
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
file('<stdin>',cls_var__app__type__eq_0) ).
fof(c_0_9_010,axiom,
! [X18,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)),X18,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),X18,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
file('<stdin>',cls_double__induction__lemma_0) ).
fof(c_0_10_011,axiom,
! [X28,X8,X14,X11] :
( c_Type_Otyping(X14,c_Lambda_OdB_OVar(X8),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X11,X14,X8,X28),X11,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
file('<stdin>',cls_var__app__typesE_0) ).
fof(c_0_11_012,axiom,
! [X28,X7,X14,X11] :
( c_Type_Otyping(X14,X7,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X11,X14,X7,X28),X11,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X28,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
file('<stdin>',cls_list__app__typeD_0) ).
fof(c_0_12_013,axiom,
! [X28,X7,X14,X11] :
( c_Type_Otyping(X14,X7,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X11,X14,X7,X28),X11,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X28,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
file('<stdin>',cls_list__app__typeE_0) ).
fof(c_0_13_014,axiom,
! [X40,X7,X12] :
( c_List_Oappend(X40,c_List_Olist_OCons(X12,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,X7,X40,tc_Lambda_OdB,tc_Lambda_OdB)),X12) = c_List_Ofoldl(c_Lambda_OdB_OApp,X7,c_List_Oappend(X40,c_List_Olist_OCons(X12,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_14_015,axiom,
! [X28,X7,X14,X29,X11] :
( c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X28,tc_Lambda_OdB,tc_Lambda_OdB),X11)
| ~ c_Type_Otypings(X14,X28,X29)
| ~ c_Type_Otyping(X14,X7,c_List_Ofoldr(c_Type_Otype_OFun,X29,X11,tc_Type_Otype,tc_Type_Otype)) ),
file('<stdin>',cls_list__app__typeI_0) ).
fof(c_0_15_016,axiom,
! [X19,X20] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X19,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X19,tc_Lambda_OdB) ),
file('<stdin>',cls_IT_OVar_0) ).
fof(c_0_16_017,axiom,
! [X28,X8,X14,X11] :
( c_Type_Otypings(X14,X28,c_Type_Osko__Type__Xvar__app__typesE__1__1(X11,X14,X8,X28))
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
file('<stdin>',cls_var__app__typesE_1) ).
fof(c_0_17_018,axiom,
! [X28,X7,X14,X11] :
( c_Type_Otypings(X14,X28,c_Type_Osko__Type__Xlist__app__typeD__1__1(X11,X14,X7,X28))
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X28,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
file('<stdin>',cls_list__app__typeD_1) ).
fof(c_0_18_019,axiom,
! [X28,X7,X14,X11] :
( c_Type_Otypings(X14,X28,c_Type_Osko__Type__Xlist__app__typeE__1__1(X11,X14,X7,X28))
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X28,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
file('<stdin>',cls_list__app__typeE_1) ).
fof(c_0_19_020,axiom,
! [X18,X12,X19,X13] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X13),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12),X18,tc_Lambda_OdB,tc_Lambda_OdB)
| X13 = X12 ),
file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_0) ).
fof(c_0_20_021,axiom,
! [X18,X12,X19,X13] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X13),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12),X18,tc_Lambda_OdB,tc_Lambda_OdB)
| X19 = X18 ),
file('<stdin>',cls_Abs__apps__eq__Abs__apps__conv_1) ).
fof(c_0_21_022,axiom,
! [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 ),
file('<stdin>',cls_Var__apps__eq__Var__apps__conv_1) ).
fof(c_0_22_023,axiom,
! [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 ),
file('<stdin>',cls_Var__apps__eq__Var__apps__conv_0) ).
fof(c_0_23_024,axiom,
! [X57,X45,X40,X3] :
( ~ class_OrderedGroup_Osemigroup__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X45),X57,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X45,X57,X3,X3)) ),
file('<stdin>',cls_foldl__assoc_0) ).
fof(c_0_24_025,axiom,
! [X28,X12,X13] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X13,X28,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X28,tc_Lambda_OdB,tc_Lambda_OdB)
| X13 = X12 ),
file('<stdin>',cls_apps__eq__tail__conv_0) ).
fof(c_0_25_026,axiom,
! [X57,X40,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X57,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X40,X57,X3,X3) ),
file('<stdin>',cls_foldl__absorb0_0) ).
fof(c_0_26_027,axiom,
! [X42,X43,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X43,X42,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X42,c_HOL_Ozero__class_Ozero(X3),X3,X3)) ),
file('<stdin>',cls_foldl__foldr1__lemma_0) ).
fof(c_0_27_028,axiom,
! [X56,X12,X13] :
( X13 != c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X13),X12),X56,tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X13),X12) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X13),X12),c_List_Oappend(X56,c_List_Olist_OCons(X12,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_28_029,axiom,
! [X42,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X42,X3,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X42,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
file('<stdin>',cls_foldl__foldr1_0) ).
fof(c_0_29_030,axiom,
! [X42,X43,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X42,X43,X3,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X43,X42,X3,X3) ),
file('<stdin>',cls_foldr__conv__foldl_0) ).
fof(c_0_30_031,axiom,
! [X6,X7,X14,X11] :
( c_Type_Otyping(X14,X7,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X11,X14,X7,X6)),X11))
| ~ c_Type_Otyping(X14,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X6),X11) ),
file('<stdin>',cls_typing__elims_I2_J_0) ).
fof(c_0_31_032,axiom,
! [X7,X12,X13] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X13),X12) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X13),X12) = X7 ),
file('<stdin>',cls_App__eq__foldl__conv_0) ).
fof(c_0_32_033,axiom,
! [X18,X12,X13] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X13)
| X12 = c_Lambda_OdB_OAbs(X13) ),
file('<stdin>',cls_apps__eq__Abs__conv_0) ).
fof(c_0_33_034,axiom,
! [X18,X12,X13] :
( c_Lambda_OdB_OAbs(X13) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X13) = X12 ),
file('<stdin>',cls_Abs__eq__apps__conv_0) ).
fof(c_0_34_035,axiom,
! [X18,X12,X21] :
( c_Lambda_OdB_OVar(X21) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X21) = X12 ),
file('<stdin>',cls_Var__eq__apps__conv_0) ).
fof(c_0_35_036,axiom,
! [X18,X12,X13] :
( c_Lambda_OdB_OAbs(X13) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB)
| X18 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_Abs__eq__apps__conv_1) ).
fof(c_0_36_037,axiom,
! [X18,X12,X13] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X13)
| X18 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_apps__eq__Abs__conv_1) ).
fof(c_0_37_038,axiom,
! [X18,X12,X21] :
( c_Lambda_OdB_OVar(X21) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB)
| X18 = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('<stdin>',cls_Var__eq__apps__conv_1) ).
fof(c_0_38_039,axiom,
! [X45,X40,X13,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X45),X40))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X13,X3,X3),X3),X40),X45)) ),
file('<stdin>',cls_rtranclp__converseD_0) ).
fof(c_0_39_040,axiom,
! [X51,X45,X42,X40,X13,X3] :
( hBOOL(hAPP(hAPP(X13,X45),X40))
| c_ListOrder_Ostep1(X13,X51,X42,X3)
| ~ c_ListOrder_Ostep1(X13,c_List_Oappend(X51,c_List_Olist_OCons(X45,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X42,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),X3) ),
file('<stdin>',cls_Snoc__step1__SnocD_1) ).
fof(c_0_40_041,axiom,
! [X51,X45,X42,X40,X13,X3] :
( X51 = X42
| c_ListOrder_Ostep1(X13,X51,X42,X3)
| ~ c_ListOrder_Ostep1(X13,c_List_Oappend(X51,c_List_Olist_OCons(X45,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X42,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),X3) ),
file('<stdin>',cls_Snoc__step1__SnocD_0) ).
fof(c_0_41_042,axiom,
! [X51,X45,X42,X40,X13,X3] :
( hBOOL(hAPP(hAPP(X13,X45),X40))
| X45 = X40
| ~ c_ListOrder_Ostep1(X13,c_List_Oappend(X51,c_List_Olist_OCons(X45,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X42,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),X3) ),
file('<stdin>',cls_Snoc__step1__SnocD_3) ).
fof(c_0_42_043,axiom,
! [X51,X45,X42,X40,X13,X3] :
( X51 = X42
| X45 = X40
| ~ c_ListOrder_Ostep1(X13,c_List_Oappend(X51,c_List_Olist_OCons(X45,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X42,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),X3) ),
file('<stdin>',cls_Snoc__step1__SnocD_2) ).
fof(c_0_43_044,axiom,
! [X45,X40,X13,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X13,X3,X3),X3),X40),X45))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X45),X40)) ),
file('<stdin>',cls_rtranclp__converseI_0) ).
fof(c_0_44_045,axiom,
! [X6,X7,X8,X14,X35,X36,X37] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X37),X36)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X7,X6,X8)))
| ~ c_Type_Otyping(X14,X6,X37)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X14,X8,X37,tc_Type_Otype),X7,X35)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
file('<stdin>',cls_MI1_0) ).
fof(c_0_45_046,axiom,
! [X6,X7,X8,X14,X35,X36,X37] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X37),X36)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X7,X6,X8)))
| ~ c_Type_Otyping(X14,X6,X36)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X14,X8,X36,tc_Type_Otype),X7,X35)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
file('<stdin>',cls_MI2_0) ).
fof(c_0_46_047,axiom,
! [X28,X7,X14,X29] :
( c_Type_Otyping(X14,X7,c_Type_Osko__Type__Xtypes__snocE__1__2(X29,X14,X7,X28))
| ~ c_Type_Otypings(X14,c_List_Oappend(X28,c_List_Olist_OCons(X7,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X29) ),
file('<stdin>',cls_types__snocE_2) ).
fof(c_0_47_048,axiom,
! [X6,X7,X8,X9,X10,X11] :
( ~ c_Type_Otyping(X9,X6,X10)
| ~ c_Type_Otyping(c_Type_Oshift(X9,X8,X10,tc_Type_Otype),X7,X11)
| c_Type_Otyping(X9,c_Lambda_Osubst(X7,X6,X8),X11) ),
file('<stdin>',cls_subst__lemma_0) ).
fof(c_0_48_049,axiom,
! [X15,X7,X41,X12] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X12),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X41),X15)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X15))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X41)) ),
file('<stdin>',cls_rtrancl__beta__App_0) ).
fof(c_0_49_050,axiom,
! [X7,X12,X13,X8] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X13,X7,X8)),c_Lambda_Osubst(X12,X7,X8)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X13),X12)) ),
file('<stdin>',cls_subst__preserves__beta_H_0) ).
fof(c_0_50_051,axiom,
! [X7,X12,X13,X8] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X7,X13,X8)),c_Lambda_Osubst(X7,X12,X8)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X13),X12)) ),
file('<stdin>',cls_subst__preserves__beta2_H_0) ).
fof(c_0_51_052,axiom,
! [X51,X45,X42,X40,X13,X3] :
( c_ListOrder_Ostep1(X13,X51,X42,X3)
| hBOOL(hAPP(hAPP(X13,X45),X40))
| ~ c_ListOrder_Ostep1(X13,c_List_Olist_OCons(X45,X51,X3),c_List_Olist_OCons(X40,X42,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_1) ).
fof(c_0_52_053,axiom,
! [X7,X30,X10,X11] :
( c_Type_Otyping(X30,c_Lambda_OdB_OAbs(X7),hAPP(hAPP(c_Type_Otype_OFun,X11),X10))
| ~ c_Type_Otyping(c_Type_Oshift(X30,c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_Type_Otype),X7,X10) ),
file('<stdin>',cls_Abs_0) ).
fof(c_0_53_054,axiom,
! [X51,X45,X42,X40,X13,X3] :
( c_ListOrder_Ostep1(X13,X51,X42,X3)
| X42 = X51
| ~ c_ListOrder_Ostep1(X13,c_List_Olist_OCons(X45,X51,X3),c_List_Olist_OCons(X40,X42,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_3) ).
fof(c_0_54_055,axiom,
! [X7,X12,X13,X8] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X7,X13,X8)),c_Lambda_Osubst(X7,X12,X8)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X13),X12)) ),
file('<stdin>',cls_subst__preserves__beta2_0) ).
fof(c_0_55_056,axiom,
! [X13,X49,X43,X58,X3] :
( hBOOL(hAPP(hAPP(X13,X49),X43))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X13,X3,X58),X43),X49)) ),
file('<stdin>',cls_conversepD_0) ).
fof(c_0_56_057,axiom,
! [X13,X59,X60,X58,X3] :
( hBOOL(hAPP(hAPP(X13,X59),X60))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X13,X3,X58),X60),X59)) ),
file('<stdin>',cls_conversep_Ocases_0) ).
fof(c_0_57_058,axiom,
! [X40,X61,X27,X13,X3] :
( c_ListOrder_Ostep1(X13,c_List_Oappend(X40,X61,X3),c_List_Oappend(X40,X27,X3),X3)
| ~ c_ListOrder_Ostep1(X13,X61,X27,X3) ),
file('<stdin>',cls_append__step1I_1) ).
fof(c_0_58_059,axiom,
! [X51,X42,X40,X13,X3] :
( ~ c_ListOrder_Ostep1(X13,X51,X42,X3)
| c_ListOrder_Ostep1(X13,c_List_Oappend(X51,X40,X3),c_List_Oappend(X42,X40,X3),X3) ),
file('<stdin>',cls_append__step1I_0) ).
fof(c_0_59_060,axiom,
! [X51,X42,X40,X13,X3] :
( c_ListOrder_Ostep1(X13,c_List_Olist_OCons(X40,X51,X3),c_List_Olist_OCons(X40,X42,X3),X3)
| ~ c_ListOrder_Ostep1(X13,X51,X42,X3) ),
file('<stdin>',cls_Cons__step1__Cons_5) ).
fof(c_0_60_061,axiom,
! [X7,X41,X12] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X12),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X41),X7)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X41)) ),
file('<stdin>',cls_rtrancl__beta__AppL_0) ).
fof(c_0_61_062,axiom,
! [X15,X7,X12] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X12),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X12),X15)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X15)) ),
file('<stdin>',cls_rtrancl__beta__AppR_0) ).
fof(c_0_62_063,axiom,
! [X7,X12,X13,X8] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X13,X7,X8)),c_Lambda_Osubst(X12,X7,X8)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X13),X12)) ),
file('<stdin>',cls_subst__preserves__beta_0) ).
fof(c_0_63_064,axiom,
! [X51,X45,X42,X40,X13,X3] :
( X40 = X45
| hBOOL(hAPP(hAPP(X13,X45),X40))
| ~ c_ListOrder_Ostep1(X13,c_List_Olist_OCons(X45,X51,X3),c_List_Olist_OCons(X40,X42,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_0) ).
fof(c_0_64_065,axiom,
! [X44,X45,X40,X13,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X40),X44))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X45),X44))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X40),X45)) ),
file('<stdin>',cls_rtranclp__trans_0) ).
fof(c_0_65_066,axiom,
! [X6,X7,X14,X11] :
( c_Type_Otyping(X14,X6,c_Type_Osko__Type__Xtyping__elims__2__1(X11,X14,X7,X6))
| ~ c_Type_Otyping(X14,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X6),X11) ),
file('<stdin>',cls_typing__elims_I2_J_1) ).
fof(c_0_66_067,axiom,
! [X51,X45,X42,X40,X13,X3] :
( X40 = X45
| X42 = X51
| ~ c_ListOrder_Ostep1(X13,c_List_Olist_OCons(X45,X51,X3),c_List_Olist_OCons(X40,X42,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_2) ).
fof(c_0_67_068,axiom,
! [X55,X50,X49,X43,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),X43),X49)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X55)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X55)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_68_069,axiom,
! [X7,X8,X14,X10,X11] :
( c_Type_Otyping(c_Type_Oshift(X14,X8,X10,tc_Type_Otype),c_Lambda_Olift(X7,X8),X11)
| ~ c_Type_Otyping(X14,X7,X11) ),
file('<stdin>',cls_lift__type_0) ).
fof(c_0_69_070,axiom,
! [X13,X49,X43,X58,X3] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X13,X3,X58),X43),X49))
| ~ hBOOL(hAPP(hAPP(X13,X49),X43)) ),
file('<stdin>',cls_conversep__iff_1) ).
fof(c_0_70_071,axiom,
! [X13,X49,X43,X58,X3] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X13,X3,X58),X49),X43))
| ~ hBOOL(hAPP(hAPP(X13,X43),X49)) ),
file('<stdin>',cls_conversep_Ointros_0) ).
fof(c_0_71_072,axiom,
! [X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X12),X6)),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X6)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X7)) ),
file('<stdin>',cls_appL_0) ).
fof(c_0_72_073,axiom,
! [X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X6),X12)),hAPP(hAPP(c_Lambda_OdB_OApp,X6),X7)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X7)) ),
file('<stdin>',cls_appR_0) ).
fof(c_0_73_074,axiom,
! [X13,X50,X49,X43,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X43),X50))
| ~ hBOOL(hAPP(hAPP(X13,X49),X50))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X43),X49)) ),
file('<stdin>',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
fof(c_0_74_075,axiom,
! [X13,X50,X49,X43,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X43),X50))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X49),X50))
| ~ hBOOL(hAPP(hAPP(X13,X43),X49)) ),
file('<stdin>',cls_converse__rtranclp__into__rtranclp_0) ).
fof(c_0_75_076,axiom,
! [X26,X8,X14,X11,X3] :
( hAPP(c_Type_Oshift(X14,X8,X11,X3),X26) = hAPP(X14,X26)
| ~ c_HOL_Oord__class_Oless(X26,X8,tc_nat) ),
file('<stdin>',cls_shift__gt_0) ).
fof(c_0_76_077,axiom,
! [X45,X56,X40,X13,X3] :
( ~ hBOOL(hAPP(hAPP(X13,X45),X56))
| c_ListOrder_Ostep1(X13,c_List_Olist_OCons(X45,X40,X3),c_List_Olist_OCons(X56,X40,X3),X3) ),
file('<stdin>',cls_Cons__step1__Cons_4) ).
fof(c_0_77_078,axiom,
! [X12,X13,X8] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X13,X8)),c_Lambda_Olift(X12,X8)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X13),X12)) ),
file('<stdin>',cls_lift__preserves__beta_H_0) ).
fof(c_0_78_079,axiom,
! [X51,X45,X42,X40,X3] :
( c_List_Oappend(X42,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X51,c_List_Olist_OCons(X45,c_List_Olist_ONil(X3),X3),X3)
| X40 = X45 ),
file('<stdin>',cls_append1__eq__conv_1) ).
fof(c_0_79_080,axiom,
! [X51,X45,X42,X40,X3] :
( c_List_Oappend(X42,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X51,c_List_Olist_OCons(X45,c_List_Olist_ONil(X3),X3),X3)
| X42 = X51 ),
file('<stdin>',cls_append1__eq__conv_0) ).
fof(c_0_80_081,axiom,
! [X50,X49,X43,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),X43),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50)),X49) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_81_082,axiom,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X43,X49,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3) ),
file('<stdin>',cls_add__less__cancel__right_0) ).
fof(c_0_82_083,axiom,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X43,X49,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3) ),
file('<stdin>',cls_add__less__cancel__left_0) ).
fof(c_0_83_084,axiom,
! [X41,X12] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X12)),c_Lambda_OdB_OAbs(X41)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X41)) ),
file('<stdin>',cls_rtrancl__beta__Abs_0) ).
fof(c_0_84_085,axiom,
! [X55,X50,X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X55),X3)
| ~ c_HOL_Oord__class_Oless(X50,X55,X3)
| ~ c_HOL_Oord__class_Oless(X43,X49,X3) ),
file('<stdin>',cls_add__strict__mono_0) ).
fof(c_0_85_086,axiom,
! [X13,X49,X43,X3] :
( c_Wellfounded_Oaccp(X13,X49,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X49),X43))
| ~ c_Wellfounded_Oaccp(X13,X43,X3) ),
file('<stdin>',cls_accp__downwards_0) ).
fof(c_0_86_087,axiom,
! [X13,X49,X43,X3] :
( c_Wellfounded_Oaccp(X13,X49,X3)
| ~ c_Wellfounded_Oaccp(X13,X43,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X49),X43)) ),
file('<stdin>',cls_accp__downwards__aux_0) ).
fof(c_0_87_088,axiom,
! [X50,X49,X43,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),X43),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_88_089,axiom,
! [X55,X50,X43,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X55)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50)),X55) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_89_090,axiom,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) ),
file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(c_0_90_091,axiom,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) ),
file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).
fof(c_0_91_092,axiom,
! [X44,X45,X40,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X45)),X44) ),
file('<stdin>',cls_class__semiring_Oadd__a_0) ).
fof(c_0_92_093,axiom,
! [X7,X12,X30,X10,X11] :
( c_Type_Otyping(X30,hAPP(hAPP(c_Lambda_OdB_OApp,X12),X7),X10)
| ~ c_Type_Otyping(X30,X7,X11)
| ~ c_Type_Otyping(X30,X12,hAPP(hAPP(c_Type_Otype_OFun,X11),X10)) ),
file('<stdin>',cls_App_0) ).
fof(c_0_93_094,axiom,
! [X15,X7,X14,X11] :
( c_Type_Otyping(X14,X15,X11)
| ~ c_Type_Otyping(X14,X7,X11)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X15)) ),
file('<stdin>',cls_subject__reduction_H_0) ).
fof(c_0_94_095,axiom,
! [X44,X45,X40,X6,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X6)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X44) = X6 ),
file('<stdin>',cls_add__cancel__21_0) ).
fof(c_0_95_096,axiom,
! [X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X49),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X49,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X43,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_add__neg__neg_0) ).
fof(c_0_96_097,axiom,
! [X49,X43,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),X43),X49),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X49,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X43,X3) ),
file('<stdin>',cls_add__pos__pos_0) ).
fof(c_0_97_098,axiom,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3)
| ~ c_HOL_Oord__class_Oless(X43,X49,X3) ),
file('<stdin>',cls_add__strict__right__mono_0) ).
fof(c_0_98_099,axiom,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3)
| ~ c_HOL_Oord__class_Oless(X43,X49,X3) ),
file('<stdin>',cls_add__less__cancel__right_1) ).
fof(c_0_99_100,axiom,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3)
| ~ c_HOL_Oord__class_Oless(X43,X49,X3) ),
file('<stdin>',cls_add__strict__left__mono_0) ).
fof(c_0_100_101,axiom,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3)
| ~ c_HOL_Oord__class_Oless(X43,X49,X3) ),
file('<stdin>',cls_add__less__cancel__left_1) ).
fof(c_0_101_102,axiom,
! [X12,X13,X8] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X13,X8)),c_Lambda_Olift(X12,X8)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X13),X12)) ),
file('<stdin>',cls_lift__preserves__beta_0) ).
fof(c_0_102_103,axiom,
! [X50,X49,X43,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50),X3)
| ~ c_HOL_Oord__class_Oless(X49,X50,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X43,X3) ),
file('<stdin>',cls_pos__add__strict_0) ).
fof(c_0_103_104,axiom,
! [X51,X42,X62,X3] :
( c_List_Olistsp(X62,c_List_Oappend(X42,X51,X3),X3)
| ~ c_List_Olistsp(X62,X51,X3)
| ~ c_List_Olistsp(X62,X42,X3) ),
file('<stdin>',cls_append__in__listsp__conv_2) ).
fof(c_0_104_105,axiom,
! [X43,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X43,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X43),X3) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(c_0_105_106,axiom,
! [X43,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X43,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X43),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(c_0_106_107,axiom,
! [X43,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X43,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X43),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_even__less__0__iff_0) ).
fof(c_0_107_108,axiom,
! [X55,X50,X43,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X55)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X55)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_108_109,axiom,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50)) ),
file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(c_0_109_110,axiom,
! [X44,X45,X40,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X44)) ),
file('<stdin>',cls_add__cancel__21_1) ).
fof(c_0_110_111,axiom,
! [X45,X40,X13,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X40),X45))
| ~ hBOOL(hAPP(hAPP(X13,X40),X45)) ),
file('<stdin>',cls_r__into__rtranclp_0) ).
fof(c_0_111_112,axiom,
! [X51,X42,X62,X3] :
( c_List_Olistsp(X62,X51,X3)
| ~ c_List_Olistsp(X62,c_List_Oappend(X42,X51,X3),X3) ),
file('<stdin>',cls_append__in__listsp__conv_1) ).
fof(c_0_112_113,axiom,
! [X51,X42,X62,X3] :
( c_List_Olistsp(X62,X42,X3)
| ~ c_List_Olistsp(X62,c_List_Oappend(X42,X51,X3),X3) ),
file('<stdin>',cls_append__in__listsp__conv_0) ).
fof(c_0_113_114,axiom,
! [X13,X26,X8] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X13,c_Lambda_OdB_OVar(X8),X26)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X13)) ),
file('<stdin>',cls_subst__Var__IT_0) ).
fof(c_0_114_115,axiom,
! [X45,X13,X43,X3] :
( c_Wellfounded_Oaccp(X13,X45,X3)
| ~ hBOOL(hAPP(hAPP(X13,X45),X43))
| ~ c_Wellfounded_Oaccp(X13,X43,X3) ),
file('<stdin>',cls_accp_Ocases_0) ).
fof(c_0_115_116,axiom,
! [X13,X49,X43,X3] :
( c_Wellfounded_Oaccp(X13,X43,X3)
| ~ hBOOL(hAPP(hAPP(X13,X43),X49))
| ~ c_Wellfounded_Oaccp(X13,X49,X3) ),
file('<stdin>',cls_accp__downward_0) ).
fof(c_0_116_117,axiom,
! [X43,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),X43),X43),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X43,X3) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(c_0_117_118,axiom,
! [X43,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X43),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X43,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(c_0_118_119,axiom,
! [X43,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X43),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X43,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_even__less__0__iff_1) ).
fof(c_0_119_120,axiom,
! [X13] :
( hBOOL(hAPP(c_InductTermi_OIT,X13))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X13,tc_Lambda_OdB) ),
file('<stdin>',cls_termi__implies__IT_0) ).
fof(c_0_120_121,axiom,
! [X15,X7,X14,X11] :
( c_Type_Otyping(X14,X15,X11)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X15))
| ~ c_Type_Otyping(X14,X7,X11) ),
file('<stdin>',cls_subject__reduction_0) ).
fof(c_0_121_122,axiom,
! [X7,X8] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X7),c_Lambda_OdB_OVar(X8))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
file('<stdin>',cls_app__Var__IT_0) ).
fof(c_0_122_123,axiom,
! [X44,X45,X40,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X40,X44,X3)
| ~ c_HOL_Oord__class_Oless(X45,X44,X3)
| ~ c_HOL_Oord__class_Oless(X40,X45,X3) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_123_124,axiom,
! [X44,X45,X40,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X44,X40,X3)
| ~ c_HOL_Oord__class_Oless(X44,X45,X3)
| ~ c_HOL_Oord__class_Oless(X45,X40,X3) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_124_125,axiom,
! [X7,X12] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X12)),c_Lambda_OdB_OAbs(X7)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X7)) ),
file('<stdin>',cls_abs_0) ).
fof(c_0_125_126,axiom,
! [X20,X21,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X21,X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X21,X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3) ),
file('<stdin>',cls_of__nat__less__iff_0) ).
fof(c_0_126_127,axiom,
! [X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3) ),
file('<stdin>',cls_of__nat__0__less__iff_0) ).
fof(c_0_127_128,axiom,
! [X20,X21,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X21,X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3)
| ~ c_HOL_Oord__class_Oless(X21,X20,tc_nat) ),
file('<stdin>',cls_of__nat__less__iff_1) ).
fof(c_0_128_129,axiom,
! [X7] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X7,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
file('<stdin>',cls_IT__implies__termi_0) ).
fof(c_0_129_130,axiom,
! [X20,X21,X48] :
( hBOOL(hAPP(hAPP(X48,X20),X21))
| c_HOL_Oord__class_Oless(X20,X21,tc_nat)
| X21 = X20
| c_HOL_Oord__class_Oless(X21,X20,tc_nat) ),
file('<stdin>',cls_nat__less__cases_0) ).
fof(c_0_130_131,axiom,
! [X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
file('<stdin>',cls_of__nat__0__less__iff_1) ).
fof(c_0_131_132,axiom,
! [X44,X45,X40,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X45) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X44)
| X45 = X44 ),
file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).
fof(c_0_132_133,axiom,
! [X49,X43,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X49,X43,X3)
| ~ c_HOL_Oord__class_Oless(X43,X49,X3) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_133_134,axiom,
! [X45,X40,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X45,X40,X3)
| ~ c_HOL_Oord__class_Oless(X40,X45,X3) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_134_135,axiom,
! [X45,X40,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X40,X45,X3)
| ~ c_HOL_Oord__class_Oless(X45,X40,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_135_136,axiom,
! [X49,X43,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X43,X49,X3)
| ~ c_HOL_Oord__class_Oless(X49,X43,X3) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_136_137,axiom,
! [X57,X51,X42,X3] :
( c_List_Oappend(X42,X51,X3) != c_List_Oappend(X42,X57,X3)
| X51 = X57 ),
file('<stdin>',cls_same__append__eq_0) ).
fof(c_0_137_138,axiom,
! [X57,X51,X42,X3] :
( c_List_Oappend(X51,X42,X3) != c_List_Oappend(X57,X42,X3)
| X51 = X57 ),
file('<stdin>',cls_append__same__eq_0) ).
fof(c_0_138_139,axiom,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X43) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X43)
| X49 = X50 ),
file('<stdin>',cls_add__right__cancel_0) ).
fof(c_0_139_140,axiom,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X49) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50)
| X49 = X50 ),
file('<stdin>',cls_add__left__cancel_0) ).
fof(c_0_140_141,axiom,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X49) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50)
| X49 = X50 ),
file('<stdin>',cls_add__imp__eq_0) ).
fof(c_0_141_142,axiom,
! [X52,X53,X54,X43,X3] :
( c_List_Olist_OCons(X43,X53,X3) != c_List_Olist_OCons(X54,X52,X3)
| X43 = X54 ),
file('<stdin>',cls_list_Oinject_0) ).
fof(c_0_142_143,axiom,
! [X52,X53,X54,X43,X3] :
( c_List_Olist_OCons(X43,X53,X3) != c_List_Olist_OCons(X54,X52,X3)
| X53 = X52 ),
file('<stdin>',cls_list_Oinject_1) ).
fof(c_0_143_144,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_144_145,axiom,
! [X6,X26,X8] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X26),X6,X8) = c_Lambda_OdB_OVar(X26)
| ~ c_HOL_Oord__class_Oless(X26,X8,tc_nat) ),
file('<stdin>',cls_subst__lt_0) ).
fof(c_0_145_146,axiom,
! [X21,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X21,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('<stdin>',cls_of__nat__less__0__iff_0) ).
fof(c_0_146_147,axiom,
! [X7,X8] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X7,X8)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
file('<stdin>',cls_lift__IT_0) ).
fof(c_0_147_148,axiom,
! [X12,X38,X8] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X8),X12,X38) = c_Lambda_OdB_OVar(X8)
| X8 = X38
| c_HOL_Oord__class_Oless(X38,X8,tc_nat) ),
file('<stdin>',cls_subst__Var_2) ).
fof(c_0_148_149,axiom,
! [X45,X40,X3] :
( ~ class_Orderings_Olinorder(X3)
| X40 = X45
| c_HOL_Oord__class_Oless(X40,X45,X3)
| c_HOL_Oord__class_Oless(X45,X40,X3) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_149_150,axiom,
! [X45,X40,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X45,X40,X3)
| X40 = X45
| c_HOL_Oord__class_Oless(X40,X45,X3) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_150_151,axiom,
! [X45,X40,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X45,X40,X3)
| c_HOL_Oord__class_Oless(X40,X45,X3)
| X40 = X45 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_151_152,axiom,
! [X45,X40,X3] :
( ~ class_Orderings_Olinorder(X3)
| X40 = X45
| c_HOL_Oord__class_Oless(X45,X40,X3)
| c_HOL_Oord__class_Oless(X40,X45,X3) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_152_153,axiom,
! [X45,X40,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X45,X40,X3)
| c_HOL_Oord__class_Oless(X40,X45,X3)
| X40 = X45 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_153_154,axiom,
! [X31,X32,X33,X34] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X34),X32) != hAPP(hAPP(c_Lambda_OdB_OApp,X33),X31)
| X32 = X31 ),
file('<stdin>',cls_dB_Osimps_I2_J_1) ).
fof(c_0_154_155,axiom,
! [X31,X32,X33,X34] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X34),X32) != hAPP(hAPP(c_Lambda_OdB_OApp,X33),X31)
| X34 = X33 ),
file('<stdin>',cls_dB_Osimps_I2_J_0) ).
fof(c_0_155_156,axiom,
! [X22,X23,X24,X25] :
( hAPP(hAPP(c_Type_Otype_OFun,X25),X23) != hAPP(hAPP(c_Type_Otype_OFun,X24),X22)
| X23 = X22 ),
file('<stdin>',cls_type_Osimps_I2_J_1) ).
fof(c_0_156_157,axiom,
! [X22,X23,X24,X25] :
( hAPP(hAPP(c_Type_Otype_OFun,X25),X23) != hAPP(hAPP(c_Type_Otype_OFun,X24),X22)
| X25 = X24 ),
file('<stdin>',cls_type_Osimps_I2_J_0) ).
fof(c_0_157_158,axiom,
! [X40,X12] :
( c_HOL_Oord__class_Oless(X40,X40,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X40),X12,X40) = X12 ),
file('<stdin>',cls_subst__Var_1) ).
fof(c_0_158_159,axiom,
! [X50,X43,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X43) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_159_160,axiom,
! [X49,X43,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X49) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X43) ),
file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).
fof(c_0_160_161,axiom,
! [X45,X40,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X45) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X40) ),
file('<stdin>',cls_class__semiring_Oadd__c_0) ).
fof(c_0_161_162,axiom,
! [X8,X14,X11] :
( hAPP(X14,X8) = X11
| ~ c_Type_Otyping(X14,c_Lambda_OdB_OVar(X8),X11) ),
file('<stdin>',cls_typing__elims_I1_J_0) ).
fof(c_0_162_163,axiom,
! [X45,X40] :
( c_HOL_Oord__class_Oless(X45,X40,tc_nat)
| c_HOL_Oord__class_Oless(X40,X45,tc_nat)
| X40 = X45 ),
file('<stdin>',cls_linorder__neqE__nat_0) ).
fof(c_0_163_164,axiom,
! [X20,X21] :
( c_HOL_Oord__class_Oless(X20,X21,tc_nat)
| c_HOL_Oord__class_Oless(X21,X20,tc_nat)
| X21 = X20 ),
file('<stdin>',cls_nat__neq__iff_0) ).
fof(c_0_164_165,axiom,
! [X38,X8] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X8),X38) = c_Lambda_OdB_OVar(X8)
| ~ c_HOL_Oord__class_Oless(X8,X38,tc_nat) ),
file('<stdin>',cls_lift_Osimps_I1_J_0) ).
fof(c_0_165_166,axiom,
! [X40,X43,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X40 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X43)
| X43 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).
fof(c_0_166_167,axiom,
! [X43,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X43) != c_HOL_Ozero__class_Ozero(X3)
| X43 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_double__eq__0__iff_0) ).
fof(c_0_167_168,axiom,
! [X51,X42,X3] :
( c_List_Oappend(X42,X51,X3) != c_List_Olist_ONil(X3)
| X51 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_append__is__Nil__conv_1) ).
fof(c_0_168_169,axiom,
! [X51,X42,X3] :
( c_List_Oappend(X42,X51,X3) != c_List_Olist_ONil(X3)
| X42 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_append__is__Nil__conv_0) ).
fof(c_0_169_170,axiom,
! [X51,X42,X3] :
( c_List_Olist_ONil(X3) != c_List_Oappend(X42,X51,X3)
| X51 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_Nil__is__append__conv_1) ).
fof(c_0_170_171,axiom,
! [X51,X42,X3] :
( c_List_Olist_ONil(X3) != c_List_Oappend(X42,X51,X3)
| X42 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_Nil__is__append__conv_0) ).
fof(c_0_171_172,axiom,
! [X40,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X40,X40,X3) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_172_173,axiom,
! [X40,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X40,X40,X3) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_173_174,axiom,
! [X40,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X40,X40,X3) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_174_175,axiom,
! [X51,X42,X3] :
( X51 != c_List_Oappend(X42,X51,X3)
| X42 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_self__append__conv2_0) ).
fof(c_0_175_176,axiom,
! [X51,X42,X3] :
( c_List_Oappend(X42,X51,X3) != X51
| X42 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_append__self__conv2_0) ).
fof(c_0_176_177,axiom,
! [X51,X42,X3] :
( X42 != c_List_Oappend(X42,X51,X3)
| X51 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_self__append__conv_0) ).
fof(c_0_177_178,axiom,
! [X51,X42,X3] :
( c_List_Oappend(X42,X51,X3) != X42
| X51 = c_List_Olist_ONil(X3) ),
file('<stdin>',cls_append__self__conv_0) ).
fof(c_0_178_179,axiom,
! [X13] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X13)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X13)) ),
file('<stdin>',cls_Lambda_0) ).
fof(c_0_179_180,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_180_181,axiom,
! [X40,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X40 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),c_HOL_Ozero__class_Ozero(X3)) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).
fof(c_0_181_182,axiom,
! [X43,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X43) = X43 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_182_183,axiom,
! [X43,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X43) = X43 ),
file('<stdin>',cls_add__0__left_0) ).
fof(c_0_183_184,axiom,
! [X43,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X43) = X43 ),
file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).
fof(c_0_184_185,axiom,
! [X40,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X40) = X40 ),
file('<stdin>',cls_class__semiring_Oadd__0_0) ).
fof(c_0_185_186,axiom,
! [X43,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),c_HOL_Ozero__class_Ozero(X3)) = X43 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_186_187,axiom,
! [X43,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),c_HOL_Ozero__class_Ozero(X3)) = X43 ),
file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).
fof(c_0_187_188,axiom,
! [X43,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),c_HOL_Ozero__class_Ozero(X3)) = X43 ),
file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).
fof(c_0_188_189,axiom,
! [X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
| X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('<stdin>',cls_gr0I_0) ).
fof(c_0_189_190,axiom,
! [X20,X21,X3] :
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X21,X3) != c_Nat_Osemiring__1__class_Oof__nat(X20,X3)
| X21 = X20 ),
file('<stdin>',cls_of__nat__eq__iff_0) ).
fof(c_0_190_191,axiom,
! [X4,X5] :
( class_Orderings_Opreorder(tc_fun(X4,X5))
| ~ class_Orderings_Opreorder(X5) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_191_192,axiom,
! [X4,X5] :
( class_Orderings_Oorder(tc_fun(X4,X5))
| ~ class_Orderings_Oorder(X5) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_192_193,axiom,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_of__nat__0_0) ).
fof(c_0_193_194,axiom,
! [X46,X47] :
( c_Lambda_OdB_OAbs(X47) != c_Lambda_OdB_OAbs(X46)
| X47 = X46 ),
file('<stdin>',cls_dB_Osimps_I3_J_0) ).
fof(c_0_194_195,axiom,
! [X16,X17] :
( c_Lambda_OdB_OVar(X17) != c_Lambda_OdB_OVar(X16)
| X17 = X16 ),
file('<stdin>',cls_dB_Osimps_I1_J_0) ).
fof(c_0_195_196,plain,
! [X27,X28,X8,X14,X10,X29,X11] :
( X10 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X11,X10,X14,X27),X11,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X10)
| ~ c_Type_Otypings(X14,X28,X29)
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X27,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_196_197,plain,
! [X39,X19,X20] :
( X39 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X20,X19,X39),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X19,tc_Lambda_OdB,tc_Lambda_OdB)),X39)) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_197_198,plain,
! [X27,X28,X8,X14,X10,X29,X11] :
( c_Type_Otypings(X14,X27,c_Type_Osko__Type__Xvar__app__types__1__1(X11,X10,X14,X27))
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X10)
| ~ c_Type_Otypings(X14,X28,X29)
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X27,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_198_199,plain,
! [X39,X19,X20] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X19,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X20,X19,X39),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X19,tc_Lambda_OdB,tc_Lambda_OdB)),X39)) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_199_200,plain,
! [X18,X19,X13] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X13,X19,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X13,X18,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X19,X18,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_200_201,plain,
! [X18,X12,X13] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X13,X18,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X13),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_201_202,plain,
! [X18,X12,X13] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X13,X18,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X13),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_202_203,plain,
! [X18,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),X18,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)),X18,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_203_204,plain,
! [X28,X8,X14,X10,X11] :
( X11 = X10
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X10)
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_204_205,plain,
! [X18,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)),X18,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),X18,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_205_206,plain,
! [X28,X8,X14,X11] :
( c_Type_Otyping(X14,c_Lambda_OdB_OVar(X8),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X11,X14,X8,X28),X11,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_206_207,plain,
! [X28,X7,X14,X11] :
( c_Type_Otyping(X14,X7,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X11,X14,X7,X28),X11,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X28,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_207_208,plain,
! [X28,X7,X14,X11] :
( c_Type_Otyping(X14,X7,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X11,X14,X7,X28),X11,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X28,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_208_209,axiom,
! [X40,X7,X12] :
( c_List_Oappend(X40,c_List_Olist_OCons(X12,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,X7,X40,tc_Lambda_OdB,tc_Lambda_OdB)),X12) = c_List_Ofoldl(c_Lambda_OdB_OApp,X7,c_List_Oappend(X40,c_List_Olist_OCons(X12,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_13 ).
fof(c_0_209_210,plain,
! [X28,X7,X14,X29,X11] :
( c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X28,tc_Lambda_OdB,tc_Lambda_OdB),X11)
| ~ c_Type_Otypings(X14,X28,X29)
| ~ c_Type_Otyping(X14,X7,c_List_Ofoldr(c_Type_Otype_OFun,X29,X11,tc_Type_Otype,tc_Type_Otype)) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_210_211,plain,
! [X19,X20] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X20),X19,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X19,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_211_212,plain,
! [X28,X8,X14,X11] :
( c_Type_Otypings(X14,X28,c_Type_Osko__Type__Xvar__app__typesE__1__1(X11,X14,X8,X28))
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X28,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_212_213,plain,
! [X28,X7,X14,X11] :
( c_Type_Otypings(X14,X28,c_Type_Osko__Type__Xlist__app__typeD__1__1(X11,X14,X7,X28))
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X28,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_213_214,plain,
! [X28,X7,X14,X11] :
( c_Type_Otypings(X14,X28,c_Type_Osko__Type__Xlist__app__typeE__1__1(X11,X14,X7,X28))
| ~ c_Type_Otyping(X14,c_List_Ofoldl(c_Lambda_OdB_OApp,X7,X28,tc_Lambda_OdB,tc_Lambda_OdB),X11) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_214_215,axiom,
! [X18,X12,X19,X13] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X13),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12),X18,tc_Lambda_OdB,tc_Lambda_OdB)
| X13 = X12 ),
c_0_19 ).
fof(c_0_215_216,axiom,
! [X18,X12,X19,X13] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X13),X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X12),X18,tc_Lambda_OdB,tc_Lambda_OdB)
| X19 = X18 ),
c_0_20 ).
fof(c_0_216_217,axiom,
! [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 ),
c_0_21 ).
fof(c_0_217_218,axiom,
! [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 ),
c_0_22 ).
fof(c_0_218_219,plain,
! [X57,X45,X40,X3] :
( ~ class_OrderedGroup_Osemigroup__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X45),X57,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X45,X57,X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_219_220,axiom,
! [X28,X12,X13] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X13,X28,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X28,tc_Lambda_OdB,tc_Lambda_OdB)
| X13 = X12 ),
c_0_24 ).
fof(c_0_220_221,plain,
! [X57,X40,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X57,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X40,X57,X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_221_222,plain,
! [X42,X43,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X43,X42,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X42,c_HOL_Ozero__class_Ozero(X3),X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_222_223,axiom,
! [X56,X12,X13] :
( X13 != c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X13),X12),X56,tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X13),X12) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X13),X12),c_List_Oappend(X56,c_List_Olist_OCons(X12,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
c_0_27 ).
fof(c_0_223_224,plain,
! [X42,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X42,X3,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X42,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_224_225,plain,
! [X42,X43,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X42,X43,X3,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X43,X42,X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_225_226,plain,
! [X6,X7,X14,X11] :
( c_Type_Otyping(X14,X7,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X11,X14,X7,X6)),X11))
| ~ c_Type_Otyping(X14,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X6),X11) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_226_227,axiom,
! [X7,X12,X13] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X13),X12) != c_List_Ofoldl(c_Lambda_OdB_OApp,X7,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X13),X12) = X7 ),
c_0_31 ).
fof(c_0_227_228,axiom,
! [X18,X12,X13] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X13)
| X12 = c_Lambda_OdB_OAbs(X13) ),
c_0_32 ).
fof(c_0_228_229,axiom,
! [X18,X12,X13] :
( c_Lambda_OdB_OAbs(X13) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X13) = X12 ),
c_0_33 ).
fof(c_0_229_230,axiom,
! [X18,X12,X21] :
( c_Lambda_OdB_OVar(X21) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X21) = X12 ),
c_0_34 ).
fof(c_0_230_231,axiom,
! [X18,X12,X13] :
( c_Lambda_OdB_OAbs(X13) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB)
| X18 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_35 ).
fof(c_0_231_232,axiom,
! [X18,X12,X13] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X13)
| X18 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_36 ).
fof(c_0_232_233,axiom,
! [X18,X12,X21] :
( c_Lambda_OdB_OVar(X21) != c_List_Ofoldl(c_Lambda_OdB_OApp,X12,X18,tc_Lambda_OdB,tc_Lambda_OdB)
| X18 = c_List_Olist_ONil(tc_Lambda_OdB) ),
c_0_37 ).
fof(c_0_233_234,plain,
! [X45,X40,X13,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X45),X40))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X13,X3,X3),X3),X40),X45)) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_234_235,plain,
! [X51,X45,X42,X40,X13,X3] :
( hBOOL(hAPP(hAPP(X13,X45),X40))
| c_ListOrder_Ostep1(X13,X51,X42,X3)
| ~ c_ListOrder_Ostep1(X13,c_List_Oappend(X51,c_List_Olist_OCons(X45,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X42,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_235_236,plain,
! [X51,X45,X42,X40,X13,X3] :
( X51 = X42
| c_ListOrder_Ostep1(X13,X51,X42,X3)
| ~ c_ListOrder_Ostep1(X13,c_List_Oappend(X51,c_List_Olist_OCons(X45,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X42,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_236_237,plain,
! [X51,X45,X42,X40,X13,X3] :
( hBOOL(hAPP(hAPP(X13,X45),X40))
| X45 = X40
| ~ c_ListOrder_Ostep1(X13,c_List_Oappend(X51,c_List_Olist_OCons(X45,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X42,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_237_238,plain,
! [X51,X45,X42,X40,X13,X3] :
( X51 = X42
| X45 = X40
| ~ c_ListOrder_Ostep1(X13,c_List_Oappend(X51,c_List_Olist_OCons(X45,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X42,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_238_239,plain,
! [X45,X40,X13,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X13,X3,X3),X3),X40),X45))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X45),X40)) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_239_240,plain,
! [X6,X7,X8,X14,X35,X36,X37] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X37),X36)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X7,X6,X8)))
| ~ c_Type_Otyping(X14,X6,X37)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X14,X8,X37,tc_Type_Otype),X7,X35)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_240_241,plain,
! [X6,X7,X8,X14,X35,X36,X37] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X37),X36)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X7,X6,X8)))
| ~ c_Type_Otyping(X14,X6,X36)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X14,X8,X36,tc_Type_Otype),X7,X35)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_241_242,plain,
! [X28,X7,X14,X29] :
( c_Type_Otyping(X14,X7,c_Type_Osko__Type__Xtypes__snocE__1__2(X29,X14,X7,X28))
| ~ c_Type_Otypings(X14,c_List_Oappend(X28,c_List_Olist_OCons(X7,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X29) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_242_243,plain,
! [X6,X7,X8,X9,X10,X11] :
( ~ c_Type_Otyping(X9,X6,X10)
| ~ c_Type_Otyping(c_Type_Oshift(X9,X8,X10,tc_Type_Otype),X7,X11)
| c_Type_Otyping(X9,c_Lambda_Osubst(X7,X6,X8),X11) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_243_244,plain,
! [X15,X7,X41,X12] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X12),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X41),X15)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X15))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X41)) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_244_245,plain,
! [X7,X12,X13,X8] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X13,X7,X8)),c_Lambda_Osubst(X12,X7,X8)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X13),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_245_246,plain,
! [X7,X12,X13,X8] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X7,X13,X8)),c_Lambda_Osubst(X7,X12,X8)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X13),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_246_247,plain,
! [X51,X45,X42,X40,X13,X3] :
( c_ListOrder_Ostep1(X13,X51,X42,X3)
| hBOOL(hAPP(hAPP(X13,X45),X40))
| ~ c_ListOrder_Ostep1(X13,c_List_Olist_OCons(X45,X51,X3),c_List_Olist_OCons(X40,X42,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_247_248,plain,
! [X7,X30,X10,X11] :
( c_Type_Otyping(X30,c_Lambda_OdB_OAbs(X7),hAPP(hAPP(c_Type_Otype_OFun,X11),X10))
| ~ c_Type_Otyping(c_Type_Oshift(X30,c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_Type_Otype),X7,X10) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_248_249,plain,
! [X51,X45,X42,X40,X13,X3] :
( c_ListOrder_Ostep1(X13,X51,X42,X3)
| X42 = X51
| ~ c_ListOrder_Ostep1(X13,c_List_Olist_OCons(X45,X51,X3),c_List_Olist_OCons(X40,X42,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_249_250,plain,
! [X7,X12,X13,X8] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X7,X13,X8)),c_Lambda_Osubst(X7,X12,X8)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X13),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_250_251,plain,
! [X13,X49,X43,X58,X3] :
( hBOOL(hAPP(hAPP(X13,X49),X43))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X13,X3,X58),X43),X49)) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_251_252,plain,
! [X13,X59,X60,X58,X3] :
( hBOOL(hAPP(hAPP(X13,X59),X60))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X13,X3,X58),X60),X59)) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_252_253,plain,
! [X40,X61,X27,X13,X3] :
( c_ListOrder_Ostep1(X13,c_List_Oappend(X40,X61,X3),c_List_Oappend(X40,X27,X3),X3)
| ~ c_ListOrder_Ostep1(X13,X61,X27,X3) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_253_254,plain,
! [X51,X42,X40,X13,X3] :
( ~ c_ListOrder_Ostep1(X13,X51,X42,X3)
| c_ListOrder_Ostep1(X13,c_List_Oappend(X51,X40,X3),c_List_Oappend(X42,X40,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_254_255,plain,
! [X51,X42,X40,X13,X3] :
( c_ListOrder_Ostep1(X13,c_List_Olist_OCons(X40,X51,X3),c_List_Olist_OCons(X40,X42,X3),X3)
| ~ c_ListOrder_Ostep1(X13,X51,X42,X3) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_255_256,plain,
! [X7,X41,X12] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X12),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X41),X7)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X41)) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_256_257,plain,
! [X15,X7,X12] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X12),X7)),hAPP(hAPP(c_Lambda_OdB_OApp,X12),X15)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X15)) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_257_258,plain,
! [X7,X12,X13,X8] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X13,X7,X8)),c_Lambda_Osubst(X12,X7,X8)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X13),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_258_259,plain,
! [X51,X45,X42,X40,X13,X3] :
( X40 = X45
| hBOOL(hAPP(hAPP(X13,X45),X40))
| ~ c_ListOrder_Ostep1(X13,c_List_Olist_OCons(X45,X51,X3),c_List_Olist_OCons(X40,X42,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_259_260,plain,
! [X44,X45,X40,X13,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X40),X44))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X45),X44))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X40),X45)) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_260_261,plain,
! [X6,X7,X14,X11] :
( c_Type_Otyping(X14,X6,c_Type_Osko__Type__Xtyping__elims__2__1(X11,X14,X7,X6))
| ~ c_Type_Otyping(X14,hAPP(hAPP(c_Lambda_OdB_OApp,X7),X6),X11) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_261_262,plain,
! [X51,X45,X42,X40,X13,X3] :
( X40 = X45
| X42 = X51
| ~ c_ListOrder_Ostep1(X13,c_List_Olist_OCons(X45,X51,X3),c_List_Olist_OCons(X40,X42,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_262_263,plain,
! [X55,X50,X49,X43,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),X43),X49)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X55)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X55)) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_263_264,plain,
! [X7,X8,X14,X10,X11] :
( c_Type_Otyping(c_Type_Oshift(X14,X8,X10,tc_Type_Otype),c_Lambda_Olift(X7,X8),X11)
| ~ c_Type_Otyping(X14,X7,X11) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_264_265,plain,
! [X13,X49,X43,X58,X3] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X13,X3,X58),X43),X49))
| ~ hBOOL(hAPP(hAPP(X13,X49),X43)) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_265_266,plain,
! [X13,X49,X43,X58,X3] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X13,X3,X58),X49),X43))
| ~ hBOOL(hAPP(hAPP(X13,X43),X49)) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_266_267,plain,
! [X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X12),X6)),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X6)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_267_268,plain,
! [X6,X7,X12] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X6),X12)),hAPP(hAPP(c_Lambda_OdB_OApp,X6),X7)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_268_269,plain,
! [X13,X50,X49,X43,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X43),X50))
| ~ hBOOL(hAPP(hAPP(X13,X49),X50))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X43),X49)) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_269_270,plain,
! [X13,X50,X49,X43,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X43),X50))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X49),X50))
| ~ hBOOL(hAPP(hAPP(X13,X43),X49)) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_270_271,plain,
! [X26,X8,X14,X11,X3] :
( hAPP(c_Type_Oshift(X14,X8,X11,X3),X26) = hAPP(X14,X26)
| ~ c_HOL_Oord__class_Oless(X26,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_271_272,plain,
! [X45,X56,X40,X13,X3] :
( ~ hBOOL(hAPP(hAPP(X13,X45),X56))
| c_ListOrder_Ostep1(X13,c_List_Olist_OCons(X45,X40,X3),c_List_Olist_OCons(X56,X40,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_272_273,plain,
! [X12,X13,X8] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X13,X8)),c_Lambda_Olift(X12,X8)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X13),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_273_274,axiom,
! [X51,X45,X42,X40,X3] :
( c_List_Oappend(X42,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X51,c_List_Olist_OCons(X45,c_List_Olist_ONil(X3),X3),X3)
| X40 = X45 ),
c_0_78 ).
fof(c_0_274_275,axiom,
! [X51,X45,X42,X40,X3] :
( c_List_Oappend(X42,c_List_Olist_OCons(X40,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X51,c_List_Olist_OCons(X45,c_List_Olist_ONil(X3),X3),X3)
| X42 = X51 ),
c_0_79 ).
fof(c_0_275_276,plain,
! [X50,X49,X43,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),X43),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50)),X49) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_276_277,plain,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X43,X49,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_277_278,plain,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X43,X49,X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_278_279,plain,
! [X41,X12] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X12)),c_Lambda_OdB_OAbs(X41)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X12),X41)) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_279_280,plain,
! [X55,X50,X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X55),X3)
| ~ c_HOL_Oord__class_Oless(X50,X55,X3)
| ~ c_HOL_Oord__class_Oless(X43,X49,X3) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_280_281,plain,
! [X13,X49,X43,X3] :
( c_Wellfounded_Oaccp(X13,X49,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X49),X43))
| ~ c_Wellfounded_Oaccp(X13,X43,X3) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_281_282,plain,
! [X13,X49,X43,X3] :
( c_Wellfounded_Oaccp(X13,X49,X3)
| ~ c_Wellfounded_Oaccp(X13,X43,X3)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X49),X43)) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_282_283,plain,
! [X50,X49,X43,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),X43),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_283_284,plain,
! [X55,X50,X43,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X55)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50)),X55) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_284_285,plain,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_285_286,plain,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X49)),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_286_287,plain,
! [X44,X45,X40,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X45)),X44) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_287_288,plain,
! [X7,X12,X30,X10,X11] :
( c_Type_Otyping(X30,hAPP(hAPP(c_Lambda_OdB_OApp,X12),X7),X10)
| ~ c_Type_Otyping(X30,X7,X11)
| ~ c_Type_Otyping(X30,X12,hAPP(hAPP(c_Type_Otype_OFun,X11),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_288_289,plain,
! [X15,X7,X14,X11] :
( c_Type_Otyping(X14,X15,X11)
| ~ c_Type_Otyping(X14,X7,X11)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X7),X15)) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_289_290,plain,
! [X44,X45,X40,X6,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X6)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X44) = X6 ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_290_291,plain,
! [X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X49),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X49,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X43,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_291_292,plain,
! [X49,X43,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),X43),X49),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X49,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X43,X3) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_292_293,plain,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3)
| ~ c_HOL_Oord__class_Oless(X43,X49,X3) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_293_294,plain,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50),X3)
| ~ c_HOL_Oord__class_Oless(X43,X49,X3) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_294_295,plain,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3)
| ~ c_HOL_Oord__class_Oless(X43,X49,X3) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_295_296,plain,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X49),X3)
| ~ c_HOL_Oord__class_Oless(X43,X49,X3) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_296_297,plain,
! [X12,X13,X8] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X13,X8)),c_Lambda_Olift(X12,X8)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X13),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_297_298,plain,
! [X50,X49,X43,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X49,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50),X3)
| ~ c_HOL_Oord__class_Oless(X49,X50,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X43,X3) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_298_299,plain,
! [X51,X42,X62,X3] :
( c_List_Olistsp(X62,c_List_Oappend(X42,X51,X3),X3)
| ~ c_List_Olistsp(X62,X51,X3)
| ~ c_List_Olistsp(X62,X42,X3) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_299_300,plain,
! [X43,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X43,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X43),X3) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_300_301,plain,
! [X43,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X43,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X43),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_301_302,plain,
! [X43,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X43,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X43),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_302_303,plain,
! [X55,X50,X43,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X55)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X55)) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_303_304,plain,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X50)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50)) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_304_305,plain,
! [X44,X45,X40,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X44)) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_305_306,plain,
! [X45,X40,X13,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X3),X40),X45))
| ~ hBOOL(hAPP(hAPP(X13,X40),X45)) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_306_307,plain,
! [X51,X42,X62,X3] :
( c_List_Olistsp(X62,X51,X3)
| ~ c_List_Olistsp(X62,c_List_Oappend(X42,X51,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_307_308,plain,
! [X51,X42,X62,X3] :
( c_List_Olistsp(X62,X42,X3)
| ~ c_List_Olistsp(X62,c_List_Oappend(X42,X51,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_308_309,plain,
! [X13,X26,X8] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X13,c_Lambda_OdB_OVar(X8),X26)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X13)) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_309_310,plain,
! [X45,X13,X43,X3] :
( c_Wellfounded_Oaccp(X13,X45,X3)
| ~ hBOOL(hAPP(hAPP(X13,X45),X43))
| ~ c_Wellfounded_Oaccp(X13,X43,X3) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_310_311,plain,
! [X13,X49,X43,X3] :
( c_Wellfounded_Oaccp(X13,X43,X3)
| ~ hBOOL(hAPP(hAPP(X13,X43),X49))
| ~ c_Wellfounded_Oaccp(X13,X49,X3) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_311_312,plain,
! [X43,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),X43),X43),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X43,X3) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_312_313,plain,
! [X43,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X43),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X43,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_313_314,plain,
! [X43,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X43),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X43,c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_314_315,plain,
! [X13] :
( hBOOL(hAPP(c_InductTermi_OIT,X13))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X13,tc_Lambda_OdB) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_315_316,plain,
! [X15,X7,X14,X11] :
( c_Type_Otyping(X14,X15,X11)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X7),X15))
| ~ c_Type_Otyping(X14,X7,X11) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_316_317,plain,
! [X7,X8] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X7),c_Lambda_OdB_OVar(X8))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_317_318,plain,
! [X44,X45,X40,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_HOL_Oord__class_Oless(X40,X44,X3)
| ~ c_HOL_Oord__class_Oless(X45,X44,X3)
| ~ c_HOL_Oord__class_Oless(X40,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_318_319,plain,
! [X44,X45,X40,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Oord__class_Oless(X44,X40,X3)
| ~ c_HOL_Oord__class_Oless(X44,X45,X3)
| ~ c_HOL_Oord__class_Oless(X45,X40,X3) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_319_320,plain,
! [X7,X12] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X12)),c_Lambda_OdB_OAbs(X7)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X12),X7)) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_320_321,plain,
! [X20,X21,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X21,X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X21,X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_321_322,plain,
! [X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_322_323,plain,
! [X20,X21,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X21,X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3)
| ~ c_HOL_Oord__class_Oless(X21,X20,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_323_324,plain,
! [X7] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X7,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_324_325,axiom,
! [X20,X21,X48] :
( hBOOL(hAPP(hAPP(X48,X20),X21))
| c_HOL_Oord__class_Oless(X20,X21,tc_nat)
| X21 = X20
| c_HOL_Oord__class_Oless(X21,X20,tc_nat) ),
c_0_129 ).
fof(c_0_325_326,plain,
! [X20,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X20,X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_326_327,plain,
! [X44,X45,X40,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X45) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X44)
| X45 = X44 ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_327_328,plain,
! [X49,X43,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X49,X43,X3)
| ~ c_HOL_Oord__class_Oless(X43,X49,X3) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_328_329,plain,
! [X45,X40,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X45,X40,X3)
| ~ c_HOL_Oord__class_Oless(X40,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_329_330,plain,
! [X45,X40,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X40,X45,X3)
| ~ c_HOL_Oord__class_Oless(X45,X40,X3) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_330_331,plain,
! [X49,X43,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X43,X49,X3)
| ~ c_HOL_Oord__class_Oless(X49,X43,X3) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_331_332,axiom,
! [X57,X51,X42,X3] :
( c_List_Oappend(X42,X51,X3) != c_List_Oappend(X42,X57,X3)
| X51 = X57 ),
c_0_136 ).
fof(c_0_332_333,axiom,
! [X57,X51,X42,X3] :
( c_List_Oappend(X51,X42,X3) != c_List_Oappend(X57,X42,X3)
| X51 = X57 ),
c_0_137 ).
fof(c_0_333_334,plain,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X43) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X43)
| X49 = X50 ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_334_335,plain,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X49) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50)
| X49 = X50 ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_335_336,plain,
! [X50,X49,X43,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X49) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50)
| X49 = X50 ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_336_337,axiom,
! [X52,X53,X54,X43,X3] :
( c_List_Olist_OCons(X43,X53,X3) != c_List_Olist_OCons(X54,X52,X3)
| X43 = X54 ),
c_0_141 ).
fof(c_0_337_338,axiom,
! [X52,X53,X54,X43,X3] :
( c_List_Olist_OCons(X43,X53,X3) != c_List_Olist_OCons(X54,X52,X3)
| X53 = X52 ),
c_0_142 ).
fof(c_0_338_339,plain,
! [X1,X2,X3] :
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_339_340,plain,
! [X6,X26,X8] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X26),X6,X8) = c_Lambda_OdB_OVar(X26)
| ~ c_HOL_Oord__class_Oless(X26,X8,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_340_341,plain,
! [X21,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X21,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_341_342,plain,
! [X7,X8] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X7,X8)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X7)) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_342_343,axiom,
! [X12,X38,X8] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X8),X12,X38) = c_Lambda_OdB_OVar(X8)
| X8 = X38
| c_HOL_Oord__class_Oless(X38,X8,tc_nat) ),
c_0_147 ).
fof(c_0_343_344,plain,
! [X45,X40,X3] :
( ~ class_Orderings_Olinorder(X3)
| X40 = X45
| c_HOL_Oord__class_Oless(X40,X45,X3)
| c_HOL_Oord__class_Oless(X45,X40,X3) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_344_345,plain,
! [X45,X40,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X45,X40,X3)
| X40 = X45
| c_HOL_Oord__class_Oless(X40,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_345_346,plain,
! [X45,X40,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_HOL_Oord__class_Oless(X45,X40,X3)
| c_HOL_Oord__class_Oless(X40,X45,X3)
| X40 = X45 ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_346_347,plain,
! [X45,X40,X3] :
( ~ class_Orderings_Olinorder(X3)
| X40 = X45
| c_HOL_Oord__class_Oless(X45,X40,X3)
| c_HOL_Oord__class_Oless(X40,X45,X3) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_347_348,plain,
! [X45,X40,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X45,X40,X3)
| c_HOL_Oord__class_Oless(X40,X45,X3)
| X40 = X45 ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_348_349,axiom,
! [X31,X32,X33,X34] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X34),X32) != hAPP(hAPP(c_Lambda_OdB_OApp,X33),X31)
| X32 = X31 ),
c_0_153 ).
fof(c_0_349_350,axiom,
! [X31,X32,X33,X34] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X34),X32) != hAPP(hAPP(c_Lambda_OdB_OApp,X33),X31)
| X34 = X33 ),
c_0_154 ).
fof(c_0_350_351,axiom,
! [X22,X23,X24,X25] :
( hAPP(hAPP(c_Type_Otype_OFun,X25),X23) != hAPP(hAPP(c_Type_Otype_OFun,X24),X22)
| X23 = X22 ),
c_0_155 ).
fof(c_0_351_352,axiom,
! [X22,X23,X24,X25] :
( hAPP(hAPP(c_Type_Otype_OFun,X25),X23) != hAPP(hAPP(c_Type_Otype_OFun,X24),X22)
| X25 = X24 ),
c_0_156 ).
fof(c_0_352_353,axiom,
! [X40,X12] :
( c_HOL_Oord__class_Oless(X40,X40,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X40),X12,X40) = X12 ),
c_0_157 ).
fof(c_0_353_354,plain,
! [X50,X43,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X50),X43) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_354_355,plain,
! [X49,X43,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X49) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X49),X43) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_355_356,plain,
! [X45,X40,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X45) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X45),X40) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_356_357,plain,
! [X8,X14,X11] :
( hAPP(X14,X8) = X11
| ~ c_Type_Otyping(X14,c_Lambda_OdB_OVar(X8),X11) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_357_358,axiom,
! [X45,X40] :
( c_HOL_Oord__class_Oless(X45,X40,tc_nat)
| c_HOL_Oord__class_Oless(X40,X45,tc_nat)
| X40 = X45 ),
c_0_162 ).
fof(c_0_358_359,axiom,
! [X20,X21] :
( c_HOL_Oord__class_Oless(X20,X21,tc_nat)
| c_HOL_Oord__class_Oless(X21,X20,tc_nat)
| X21 = X20 ),
c_0_163 ).
fof(c_0_359_360,plain,
! [X38,X8] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X8),X38) = c_Lambda_OdB_OVar(X8)
| ~ c_HOL_Oord__class_Oless(X8,X38,tc_nat) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_360_361,plain,
! [X40,X43,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X40 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),X43)
| X43 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_361_362,plain,
! [X43,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),X43) != c_HOL_Ozero__class_Ozero(X3)
| X43 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_362_363,axiom,
! [X51,X42,X3] :
( c_List_Oappend(X42,X51,X3) != c_List_Olist_ONil(X3)
| X51 = c_List_Olist_ONil(X3) ),
c_0_167 ).
fof(c_0_363_364,axiom,
! [X51,X42,X3] :
( c_List_Oappend(X42,X51,X3) != c_List_Olist_ONil(X3)
| X42 = c_List_Olist_ONil(X3) ),
c_0_168 ).
fof(c_0_364_365,axiom,
! [X51,X42,X3] :
( c_List_Olist_ONil(X3) != c_List_Oappend(X42,X51,X3)
| X51 = c_List_Olist_ONil(X3) ),
c_0_169 ).
fof(c_0_365_366,axiom,
! [X51,X42,X3] :
( c_List_Olist_ONil(X3) != c_List_Oappend(X42,X51,X3)
| X42 = c_List_Olist_ONil(X3) ),
c_0_170 ).
fof(c_0_366_367,plain,
! [X40,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X40,X40,X3) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_367_368,plain,
! [X40,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X40,X40,X3) ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_368_369,plain,
! [X40,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X40,X40,X3) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_369_370,axiom,
! [X51,X42,X3] :
( X51 != c_List_Oappend(X42,X51,X3)
| X42 = c_List_Olist_ONil(X3) ),
c_0_174 ).
fof(c_0_370_371,axiom,
! [X51,X42,X3] :
( c_List_Oappend(X42,X51,X3) != X51
| X42 = c_List_Olist_ONil(X3) ),
c_0_175 ).
fof(c_0_371_372,axiom,
! [X51,X42,X3] :
( X42 != c_List_Oappend(X42,X51,X3)
| X51 = c_List_Olist_ONil(X3) ),
c_0_176 ).
fof(c_0_372_373,axiom,
! [X51,X42,X3] :
( c_List_Oappend(X42,X51,X3) != X42
| X51 = c_List_Olist_ONil(X3) ),
c_0_177 ).
fof(c_0_373_374,plain,
! [X13] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X13)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X13)) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_374_375,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_179]) ).
fof(c_0_375_376,plain,
! [X40,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X40 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X40),c_HOL_Ozero__class_Ozero(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_376_377,plain,
! [X43,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X43) = X43 ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_377_378,plain,
! [X43,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X43) = X43 ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_378_379,plain,
! [X43,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X43) = X43 ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_379_380,plain,
! [X40,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X40) = X40 ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_380_381,plain,
! [X43,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),c_HOL_Ozero__class_Ozero(X3)) = X43 ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_381_382,plain,
! [X43,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),c_HOL_Ozero__class_Ozero(X3)) = X43 ),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_382_383,plain,
! [X43,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X43),c_HOL_Ozero__class_Ozero(X3)) = X43 ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_383_384,axiom,
! [X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat)
| X20 = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_188 ).
fof(c_0_384_385,plain,
! [X20,X21,X3] :
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X21,X3) != c_Nat_Osemiring__1__class_Oof__nat(X20,X3)
| X21 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_385_386,plain,
! [X4,X5] :
( class_Orderings_Opreorder(tc_fun(X4,X5))
| ~ class_Orderings_Opreorder(X5) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_386_387,plain,
! [X4,X5] :
( class_Orderings_Oorder(tc_fun(X4,X5))
| ~ class_Orderings_Oorder(X5) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_387_388,plain,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_388_389,axiom,
! [X46,X47] :
( c_Lambda_OdB_OAbs(X47) != c_Lambda_OdB_OAbs(X46)
| X47 = X46 ),
c_0_193 ).
fof(c_0_389_390,axiom,
! [X16,X17] :
( c_Lambda_OdB_OVar(X17) != c_Lambda_OdB_OVar(X16)
| X17 = X16 ),
c_0_194 ).
fof(c_0_390_391,plain,
! [X30,X31,X32,X33,X34,X35,X36] :
( X34 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X36,X34,X33,X30),X36,tc_Type_Otype,tc_Type_Otype)
| ~ c_Type_Otyping(X33,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X31,tc_Lambda_OdB,tc_Lambda_OdB),X34)
| ~ c_Type_Otypings(X33,X31,X35)
| ~ c_Type_Otyping(X33,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X31,tc_Lambda_OdB,tc_Lambda_OdB),X30,tc_Lambda_OdB,tc_Lambda_OdB),X36) ),
inference(variable_rename,[status(thm)],[c_0_195]) ).
fof(c_0_391_392,plain,
! [X40,X41,X42] :
( X40 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X42),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X42,X41,X40),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X42),X41,tc_Lambda_OdB,tc_Lambda_OdB)),X40)) ),
inference(variable_rename,[status(thm)],[c_0_196]) ).
fof(c_0_392_393,plain,
! [X30,X31,X32,X33,X34,X35,X36] :
( c_Type_Otypings(X33,X30,c_Type_Osko__Type__Xvar__app__types__1__1(X36,X34,X33,X30))
| ~ c_Type_Otyping(X33,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X31,tc_Lambda_OdB,tc_Lambda_OdB),X34)
| ~ c_Type_Otypings(X33,X31,X35)
| ~ c_Type_Otyping(X33,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X32),X31,tc_Lambda_OdB,tc_Lambda_OdB),X30,tc_Lambda_OdB,tc_Lambda_OdB),X36) ),
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_393_394,plain,
! [X40,X41,X42] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X41,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X42,X41,X40),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X42),X41,tc_Lambda_OdB,tc_Lambda_OdB)),X40)) ),
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_394_395,plain,
! [X20,X21,X22] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X22,X21,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X22,X20,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X21,X20,tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_199])])]) ).
fof(c_0_395_396,plain,
! [X19,X20,X21] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X21,X19,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X19,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_200]) ).
fof(c_0_396_397,plain,
! [X19,X20,X21] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X21,X19,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X19,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_397_398,plain,
! [X19,X20,X21] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X21)),X20),X19,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X20))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X21,X20,c_HOL_Ozero__class_Ozero(tc_nat)),X19,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(variable_rename,[status(thm)],[c_0_202]) ).
fof(c_0_398_399,plain,
! [X29,X30,X31,X32,X33] :
( X33 = X32
| ~ c_Type_Otyping(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X30),X29,tc_Lambda_OdB,tc_Lambda_OdB),X32)
| ~ c_Type_Otyping(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X30),X29,tc_Lambda_OdB,tc_Lambda_OdB),X33) ),
inference(variable_rename,[status(thm)],[c_0_203]) ).
fof(c_0_399_400,plain,
! [X19,X20,X21] :
( ~ 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(X21,X20,c_HOL_Ozero__class_Ozero(tc_nat)),X19,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X20,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(X21)),X20),X19,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_204]) ).
fof(c_0_400_401,plain,
! [X29,X30,X31,X32] :
( c_Type_Otyping(X31,c_Lambda_OdB_OVar(X30),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X32,X31,X30,X29),X32,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X30),X29,tc_Lambda_OdB,tc_Lambda_OdB),X32) ),
inference(variable_rename,[status(thm)],[c_0_205]) ).
fof(c_0_401_402,plain,
! [X29,X30,X31,X32] :
( c_Type_Otyping(X31,X30,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X32,X31,X30,X29),X32,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X29,tc_Lambda_OdB,tc_Lambda_OdB),X32) ),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_402_403,plain,
! [X29,X30,X31,X32] :
( c_Type_Otyping(X31,X30,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X32,X31,X30,X29),X32,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X29,tc_Lambda_OdB,tc_Lambda_OdB),X32) ),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_403_404,plain,
! [X41,X42,X43] :
( c_List_Oappend(X41,c_List_Olist_OCons(X43,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,X42,X41,tc_Lambda_OdB,tc_Lambda_OdB)),X43) = c_List_Ofoldl(c_Lambda_OdB_OApp,X42,c_List_Oappend(X41,c_List_Olist_OCons(X43,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_208]) ).
fof(c_0_404_405,plain,
! [X30,X31,X32,X33,X34] :
( c_Type_Otyping(X32,c_List_Ofoldl(c_Lambda_OdB_OApp,X31,X30,tc_Lambda_OdB,tc_Lambda_OdB),X34)
| ~ c_Type_Otypings(X32,X30,X33)
| ~ c_Type_Otyping(X32,X31,c_List_Ofoldr(c_Type_Otype_OFun,X33,X34,tc_Type_Otype,tc_Type_Otype)) ),
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_405_406,plain,
! [X21,X22] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X22),X21,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X21,tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_210])])]) ).
fof(c_0_406_407,plain,
! [X29,X30,X31,X32] :
( c_Type_Otypings(X31,X29,c_Type_Osko__Type__Xvar__app__typesE__1__1(X32,X31,X30,X29))
| ~ c_Type_Otyping(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X30),X29,tc_Lambda_OdB,tc_Lambda_OdB),X32) ),
inference(variable_rename,[status(thm)],[c_0_211]) ).
fof(c_0_407_408,plain,
! [X29,X30,X31,X32] :
( c_Type_Otypings(X31,X29,c_Type_Osko__Type__Xlist__app__typeD__1__1(X32,X31,X30,X29))
| ~ c_Type_Otyping(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X29,tc_Lambda_OdB,tc_Lambda_OdB),X32) ),
inference(variable_rename,[status(thm)],[c_0_212]) ).
fof(c_0_408_409,plain,
! [X29,X30,X31,X32] :
( c_Type_Otypings(X31,X29,c_Type_Osko__Type__Xlist__app__typeE__1__1(X32,X31,X30,X29))
| ~ c_Type_Otyping(X31,c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X29,tc_Lambda_OdB,tc_Lambda_OdB),X32) ),
inference(variable_rename,[status(thm)],[c_0_213]) ).
fof(c_0_409_410,plain,
! [X20,X21,X22,X23] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),X22,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X21),X20,tc_Lambda_OdB,tc_Lambda_OdB)
| X23 = X21 ),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_410_411,plain,
! [X20,X21,X22,X23] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23),X22,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X21),X20,tc_Lambda_OdB,tc_Lambda_OdB)
| X22 = X20 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_215])])]) ).
fof(c_0_411_412,plain,
! [X22,X23,X24,X25] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X25),X23,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X24),X22,tc_Lambda_OdB,tc_Lambda_OdB)
| X23 = X22 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_216])])]) ).
fof(c_0_412_413,plain,
! [X22,X23,X24,X25] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X25),X23,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X24),X22,tc_Lambda_OdB,tc_Lambda_OdB)
| X25 = X24 ),
inference(variable_rename,[status(thm)],[c_0_217]) ).
fof(c_0_413_414,plain,
! [X58,X59,X60,X61] :
( ~ class_OrderedGroup_Osemigroup__add(X61)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X61),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),X60),X59),X58,X61,X61) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),X60),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X61),X59,X58,X61,X61)) ),
inference(variable_rename,[status(thm)],[c_0_218]) ).
fof(c_0_414_415,plain,
! [X29,X30,X31] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X31,X29,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X29,tc_Lambda_OdB,tc_Lambda_OdB)
| X31 = X30 ),
inference(variable_rename,[status(thm)],[c_0_219]) ).
fof(c_0_415_416,plain,
! [X58,X59,X60] :
( ~ class_OrderedGroup_Omonoid__add(X60)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X59),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X60),c_HOL_Ozero__class_Ozero(X60),X58,X60,X60)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X60),X59,X58,X60,X60) ),
inference(variable_rename,[status(thm)],[c_0_220]) ).
fof(c_0_416_417,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_221]) ).
fof(c_0_417_418,plain,
! [X57,X58,X59] :
( X59 != c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X59),X58),X57,tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X59),X58) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X59),X58),c_List_Oappend(X57,c_List_Olist_OCons(X58,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_222]) ).
fof(c_0_418_419,plain,
! [X43,X44] :
( ~ class_OrderedGroup_Omonoid__add(X44)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X44),c_HOL_Ozero__class_Ozero(X44),X43,X44,X44) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X44),X43,c_HOL_Ozero__class_Ozero(X44),X44,X44) ),
inference(variable_rename,[status(thm)],[c_0_223]) ).
fof(c_0_419_420,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_224]) ).
fof(c_0_420_421,plain,
! [X15,X16,X17,X18] :
( c_Type_Otyping(X17,X16,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X18,X17,X16,X15)),X18))
| ~ c_Type_Otyping(X17,hAPP(hAPP(c_Lambda_OdB_OApp,X16),X15),X18) ),
inference(variable_rename,[status(thm)],[c_0_225]) ).
fof(c_0_421_422,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X16),X15) != c_List_Ofoldl(c_Lambda_OdB_OApp,X14,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,X16),X15) = X14 ),
inference(variable_rename,[status(thm)],[c_0_226]) ).
fof(c_0_422_423,plain,
! [X19,X20,X21] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X21)
| X20 = c_Lambda_OdB_OAbs(X21) ),
inference(variable_rename,[status(thm)],[c_0_227]) ).
fof(c_0_423_424,plain,
! [X19,X20,X21] :
( c_Lambda_OdB_OAbs(X21) != c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X19,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(X21) = X20 ),
inference(variable_rename,[status(thm)],[c_0_228]) ).
fof(c_0_424_425,plain,
! [X22,X23,X24] :
( c_Lambda_OdB_OVar(X24) != c_List_Ofoldl(c_Lambda_OdB_OApp,X23,X22,tc_Lambda_OdB,tc_Lambda_OdB)
| c_Lambda_OdB_OVar(X24) = X23 ),
inference(variable_rename,[status(thm)],[c_0_229]) ).
fof(c_0_425_426,plain,
! [X19,X20,X21] :
( c_Lambda_OdB_OAbs(X21) != c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X19,tc_Lambda_OdB,tc_Lambda_OdB)
| X19 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_230])])]) ).
fof(c_0_426_427,plain,
! [X19,X20,X21] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,X20,X19,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X21)
| X19 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_231])])]) ).
fof(c_0_427_428,plain,
! [X22,X23,X24] :
( c_Lambda_OdB_OVar(X24) != c_List_Ofoldl(c_Lambda_OdB_OApp,X23,X22,tc_Lambda_OdB,tc_Lambda_OdB)
| X22 = c_List_Olist_ONil(tc_Lambda_OdB) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_232])])]) ).
fof(c_0_428_429,plain,
! [X46,X47,X48,X49] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X48,X49),X46),X47))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X48,X49,X49),X49),X47),X46)) ),
inference(variable_rename,[status(thm)],[c_0_233]) ).
fof(c_0_429_430,plain,
! [X52,X53,X54,X55,X56,X57] :
( hBOOL(hAPP(hAPP(X56,X53),X55))
| c_ListOrder_Ostep1(X56,X52,X54,X57)
| ~ c_ListOrder_Ostep1(X56,c_List_Oappend(X52,c_List_Olist_OCons(X53,c_List_Olist_ONil(X57),X57),X57),c_List_Oappend(X54,c_List_Olist_OCons(X55,c_List_Olist_ONil(X57),X57),X57),X57) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_234])])]) ).
fof(c_0_430_431,plain,
! [X52,X53,X54,X55,X56,X57] :
( X52 = X54
| c_ListOrder_Ostep1(X56,X52,X54,X57)
| ~ c_ListOrder_Ostep1(X56,c_List_Oappend(X52,c_List_Olist_OCons(X53,c_List_Olist_ONil(X57),X57),X57),c_List_Oappend(X54,c_List_Olist_OCons(X55,c_List_Olist_ONil(X57),X57),X57),X57) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_235])])]) ).
fof(c_0_431_432,plain,
! [X52,X53,X54,X55,X56,X57] :
( hBOOL(hAPP(hAPP(X56,X53),X55))
| X53 = X55
| ~ c_ListOrder_Ostep1(X56,c_List_Oappend(X52,c_List_Olist_OCons(X53,c_List_Olist_ONil(X57),X57),X57),c_List_Oappend(X54,c_List_Olist_OCons(X55,c_List_Olist_ONil(X57),X57),X57),X57) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_236])])]) ).
fof(c_0_432_433,plain,
! [X52,X53,X54,X55,X56,X57] :
( X52 = X54
| X53 = X55
| ~ c_ListOrder_Ostep1(X56,c_List_Oappend(X52,c_List_Olist_OCons(X53,c_List_Olist_ONil(X57),X57),X57),c_List_Oappend(X54,c_List_Olist_OCons(X55,c_List_Olist_ONil(X57),X57),X57),X57) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_237])])]) ).
fof(c_0_433_434,plain,
! [X46,X47,X48,X49] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X48,X49,X49),X49),X47),X46))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X48,X49),X46),X47)) ),
inference(variable_rename,[status(thm)],[c_0_238]) ).
fof(c_0_434_435,plain,
! [X38,X39,X40,X41,X42,X43,X44] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X44),X43)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X39,X38,X40)))
| ~ c_Type_Otyping(X41,X38,X44)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X38))
| ~ c_Type_Otyping(c_Type_Oshift(X41,X40,X44,tc_Type_Otype),X39,X42)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X39)) ),
inference(variable_rename,[status(thm)],[c_0_239]) ).
fof(c_0_435_436,plain,
! [X38,X39,X40,X41,X42,X43,X44] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X44),X43)
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X39,X38,X40)))
| ~ c_Type_Otyping(X41,X38,X43)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X38))
| ~ c_Type_Otyping(c_Type_Oshift(X41,X40,X43,tc_Type_Otype),X39,X42)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X39)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_240])])]) ).
fof(c_0_436_437,plain,
! [X30,X31,X32,X33] :
( c_Type_Otyping(X32,X31,c_Type_Osko__Type__Xtypes__snocE__1__2(X33,X32,X31,X30))
| ~ c_Type_Otypings(X32,c_List_Oappend(X30,c_List_Olist_OCons(X31,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X33) ),
inference(variable_rename,[status(thm)],[c_0_241]) ).
fof(c_0_437_438,plain,
! [X12,X13,X14,X15,X16,X17] :
( ~ c_Type_Otyping(X15,X12,X16)
| ~ c_Type_Otyping(c_Type_Oshift(X15,X14,X16,tc_Type_Otype),X13,X17)
| c_Type_Otyping(X15,c_Lambda_Osubst(X13,X12,X14),X17) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_242])])]) ).
fof(c_0_438_439,plain,
! [X42,X43,X44,X45] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X45),X43)),hAPP(hAPP(c_Lambda_OdB_OApp,X44),X42)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X43),X42))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X45),X44)) ),
inference(variable_rename,[status(thm)],[c_0_243]) ).
fof(c_0_439_440,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X16,X14,X17)),c_Lambda_Osubst(X15,X14,X17)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X16),X15)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_244])])]) ).
fof(c_0_440_441,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X14,X16,X17)),c_Lambda_Osubst(X14,X15,X17)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X16),X15)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_245])])]) ).
fof(c_0_441_442,plain,
! [X52,X53,X54,X55,X56,X57] :
( c_ListOrder_Ostep1(X56,X52,X54,X57)
| hBOOL(hAPP(hAPP(X56,X53),X55))
| ~ c_ListOrder_Ostep1(X56,c_List_Olist_OCons(X53,X52,X57),c_List_Olist_OCons(X55,X54,X57),X57) ),
inference(variable_rename,[status(thm)],[c_0_246]) ).
fof(c_0_442_443,plain,
! [X31,X32,X33,X34] :
( c_Type_Otyping(X32,c_Lambda_OdB_OAbs(X31),hAPP(hAPP(c_Type_Otype_OFun,X34),X33))
| ~ c_Type_Otyping(c_Type_Oshift(X32,c_HOL_Ozero__class_Ozero(tc_nat),X34,tc_Type_Otype),X31,X33) ),
inference(variable_rename,[status(thm)],[c_0_247]) ).
fof(c_0_443_444,plain,
! [X52,X53,X54,X55,X56,X57] :
( c_ListOrder_Ostep1(X56,X52,X54,X57)
| X54 = X52
| ~ c_ListOrder_Ostep1(X56,c_List_Olist_OCons(X53,X52,X57),c_List_Olist_OCons(X55,X54,X57),X57) ),
inference(variable_rename,[status(thm)],[c_0_248]) ).
fof(c_0_444_445,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X14,X16,X17)),c_Lambda_Osubst(X14,X15,X17)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X16),X15)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_249])])]) ).
fof(c_0_445_446,plain,
! [X59,X60,X61,X62,X63] :
( hBOOL(hAPP(hAPP(X59,X60),X61))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X59,X63,X62),X61),X60)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_250])])]) ).
fof(c_0_446_447,plain,
! [X61,X62,X63,X64,X65] :
( hBOOL(hAPP(hAPP(X61,X62),X63))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X61,X65,X64),X63),X62)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_251])])]) ).
fof(c_0_447_448,plain,
! [X62,X63,X64,X65,X66] :
( c_ListOrder_Ostep1(X65,c_List_Oappend(X62,X63,X66),c_List_Oappend(X62,X64,X66),X66)
| ~ c_ListOrder_Ostep1(X65,X63,X64,X66) ),
inference(variable_rename,[status(thm)],[c_0_252]) ).
fof(c_0_448_449,plain,
! [X52,X53,X54,X55,X56] :
( ~ c_ListOrder_Ostep1(X55,X52,X53,X56)
| c_ListOrder_Ostep1(X55,c_List_Oappend(X52,X54,X56),c_List_Oappend(X53,X54,X56),X56) ),
inference(variable_rename,[status(thm)],[c_0_253]) ).
fof(c_0_449_450,plain,
! [X52,X53,X54,X55,X56] :
( c_ListOrder_Ostep1(X55,c_List_Olist_OCons(X54,X52,X56),c_List_Olist_OCons(X54,X53,X56),X56)
| ~ c_ListOrder_Ostep1(X55,X52,X53,X56) ),
inference(variable_rename,[status(thm)],[c_0_254]) ).
fof(c_0_450_451,plain,
! [X42,X43,X44] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X44),X42)),hAPP(hAPP(c_Lambda_OdB_OApp,X43),X42)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X44),X43)) ),
inference(variable_rename,[status(thm)],[c_0_255]) ).
fof(c_0_451_452,plain,
! [X16,X17,X18] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X18),X17)),hAPP(hAPP(c_Lambda_OdB_OApp,X18),X16)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X17),X16)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_256])])]) ).
fof(c_0_452_453,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X16,X14,X17)),c_Lambda_Osubst(X15,X14,X17)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X16),X15)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_257])])]) ).
fof(c_0_453_454,plain,
! [X52,X53,X54,X55,X56,X57] :
( X55 = X53
| hBOOL(hAPP(hAPP(X56,X53),X55))
| ~ c_ListOrder_Ostep1(X56,c_List_Olist_OCons(X53,X52,X57),c_List_Olist_OCons(X55,X54,X57),X57) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_258])])]) ).
fof(c_0_454_455,plain,
! [X46,X47,X48,X49,X50] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X49,X50),X48),X46))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X49,X50),X47),X46))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X49,X50),X48),X47)) ),
inference(variable_rename,[status(thm)],[c_0_259]) ).
fof(c_0_455_456,plain,
! [X15,X16,X17,X18] :
( c_Type_Otyping(X17,X15,c_Type_Osko__Type__Xtyping__elims__2__1(X18,X17,X16,X15))
| ~ c_Type_Otyping(X17,hAPP(hAPP(c_Lambda_OdB_OApp,X16),X15),X18) ),
inference(variable_rename,[status(thm)],[c_0_260]) ).
fof(c_0_456_457,plain,
! [X52,X53,X54,X55,X56,X57] :
( X55 = X53
| X54 = X52
| ~ c_ListOrder_Ostep1(X56,c_List_Olist_OCons(X53,X52,X57),c_List_Olist_OCons(X55,X54,X57),X57) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_261])])]) ).
fof(c_0_457_458,plain,
! [X56,X57,X58,X59,X60] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X60)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X59),X58)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X57),X56)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X59),X57)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X58),X56)) ),
inference(variable_rename,[status(thm)],[c_0_262]) ).
fof(c_0_458_459,plain,
! [X15,X16,X17,X18,X19] :
( c_Type_Otyping(c_Type_Oshift(X17,X16,X18,tc_Type_Otype),c_Lambda_Olift(X15,X16),X19)
| ~ c_Type_Otyping(X17,X15,X19) ),
inference(variable_rename,[status(thm)],[c_0_263]) ).
fof(c_0_459_460,plain,
! [X59,X60,X61,X62,X63] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X59,X63,X62),X61),X60))
| ~ hBOOL(hAPP(hAPP(X59,X60),X61)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_264])])]) ).
fof(c_0_460_461,plain,
! [X59,X60,X61,X62,X63] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X59,X63,X62),X60),X61))
| ~ hBOOL(hAPP(hAPP(X59,X61),X60)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_265])])]) ).
fof(c_0_461_462,plain,
! [X13,X14,X15] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X15),X13)),hAPP(hAPP(c_Lambda_OdB_OApp,X14),X13)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X15),X14)) ),
inference(variable_rename,[status(thm)],[c_0_266]) ).
fof(c_0_462_463,plain,
! [X13,X14,X15] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X13),X15)),hAPP(hAPP(c_Lambda_OdB_OApp,X13),X14)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X15),X14)) ),
inference(variable_rename,[status(thm)],[c_0_267]) ).
fof(c_0_463_464,plain,
! [X51,X52,X53,X54,X55] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X51,X55),X54),X52))
| ~ hBOOL(hAPP(hAPP(X51,X53),X52))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X51,X55),X54),X53)) ),
inference(variable_rename,[status(thm)],[c_0_268]) ).
fof(c_0_464_465,plain,
! [X51,X52,X53,X54,X55] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X51,X55),X54),X52))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X51,X55),X53),X52))
| ~ hBOOL(hAPP(hAPP(X51,X54),X53)) ),
inference(variable_rename,[status(thm)],[c_0_269]) ).
fof(c_0_465_466,plain,
! [X27,X28,X29,X30,X31] :
( hAPP(c_Type_Oshift(X29,X28,X30,X31),X27) = hAPP(X29,X27)
| ~ c_HOL_Oord__class_Oless(X27,X28,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_270])])]) ).
fof(c_0_466_467,plain,
! [X57,X58,X59,X60,X61] :
( ~ hBOOL(hAPP(hAPP(X60,X57),X58))
| c_ListOrder_Ostep1(X60,c_List_Olist_OCons(X57,X59,X61),c_List_Olist_OCons(X58,X59,X61),X61) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_271])])]) ).
fof(c_0_467_468,plain,
! [X14,X15,X16] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X15,X16)),c_Lambda_Olift(X14,X16)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X15),X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_272])])]) ).
fof(c_0_468_469,plain,
! [X52,X53,X54,X55,X56] :
( c_List_Oappend(X54,c_List_Olist_OCons(X55,c_List_Olist_ONil(X56),X56),X56) != c_List_Oappend(X52,c_List_Olist_OCons(X53,c_List_Olist_ONil(X56),X56),X56)
| X55 = X53 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_273])])]) ).
fof(c_0_469_470,plain,
! [X52,X53,X54,X55,X56] :
( c_List_Oappend(X54,c_List_Olist_OCons(X55,c_List_Olist_ONil(X56),X56),X56) != c_List_Oappend(X52,c_List_Olist_OCons(X53,c_List_Olist_ONil(X56),X56),X56)
| X54 = X52 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_274])])]) ).
fof(c_0_470_471,plain,
! [X51,X52,X53,X54] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X52)),X51) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51)),X52) ),
inference(variable_rename,[status(thm)],[c_0_275]) ).
fof(c_0_471_472,plain,
! [X51,X52,X53,X54] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
| c_HOL_Oord__class_Oless(X53,X52,X54)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51),X54) ),
inference(variable_rename,[status(thm)],[c_0_276]) ).
fof(c_0_472_473,plain,
! [X51,X52,X53,X54] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
| c_HOL_Oord__class_Oless(X53,X52,X54)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X52),X54) ),
inference(variable_rename,[status(thm)],[c_0_277]) ).
fof(c_0_473_474,plain,
! [X42,X43] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X43)),c_Lambda_OdB_OAbs(X42)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X43),X42)) ),
inference(variable_rename,[status(thm)],[c_0_278]) ).
fof(c_0_474_475,plain,
! [X56,X57,X58,X59,X60] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X60)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X59),X57),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X60),X58),X56),X60)
| ~ c_HOL_Oord__class_Oless(X57,X56,X60)
| ~ c_HOL_Oord__class_Oless(X59,X58,X60) ),
inference(variable_rename,[status(thm)],[c_0_279]) ).
fof(c_0_475_476,plain,
! [X50,X51,X52,X53] :
( c_Wellfounded_Oaccp(X50,X51,X53)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X50,X53),X51),X52))
| ~ c_Wellfounded_Oaccp(X50,X52,X53) ),
inference(variable_rename,[status(thm)],[c_0_280]) ).
fof(c_0_476_477,plain,
! [X50,X51,X52,X53] :
( c_Wellfounded_Oaccp(X50,X51,X53)
| ~ c_Wellfounded_Oaccp(X50,X52,X53)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X50,X53),X51),X52)) ),
inference(variable_rename,[status(thm)],[c_0_281]) ).
fof(c_0_477_478,plain,
! [X51,X52,X53,X54] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X52)),X51) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51)) ),
inference(variable_rename,[status(thm)],[c_0_282]) ).
fof(c_0_478_479,plain,
! [X56,X57,X58,X59] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X59)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X58),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X57),X56)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X58),X57)),X56) ),
inference(variable_rename,[status(thm)],[c_0_283]) ).
fof(c_0_479_480,plain,
! [X51,X52,X53,X54] :
( ~ class_OrderedGroup_Oab__semigroup__add(X54)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X52)),X51) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51)) ),
inference(variable_rename,[status(thm)],[c_0_284]) ).
fof(c_0_480_481,plain,
! [X51,X52,X53,X54] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X54)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X52)),X51) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51)) ),
inference(variable_rename,[status(thm)],[c_0_285]) ).
fof(c_0_481_482,plain,
! [X46,X47,X48,X49] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X49)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X46)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X47)),X46) ),
inference(variable_rename,[status(thm)],[c_0_286]) ).
fof(c_0_482_483,plain,
! [X31,X32,X33,X34,X35] :
( c_Type_Otyping(X33,hAPP(hAPP(c_Lambda_OdB_OApp,X32),X31),X34)
| ~ c_Type_Otyping(X33,X31,X35)
| ~ c_Type_Otyping(X33,X32,hAPP(hAPP(c_Type_Otype_OFun,X35),X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_287])])]) ).
fof(c_0_483_484,plain,
! [X16,X17,X18,X19] :
( c_Type_Otyping(X18,X16,X19)
| ~ c_Type_Otyping(X18,X17,X19)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X17),X16)) ),
inference(variable_rename,[status(thm)],[c_0_288]) ).
fof(c_0_484_485,plain,
! [X46,X47,X48,X49,X50] :
( ~ class_OrderedGroup_Oab__group__add(X50)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X50),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X50),X47),X46)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X50),X47),X49)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X50),X48),X46) = X49 ),
inference(variable_rename,[status(thm)],[c_0_289]) ).
fof(c_0_485_486,plain,
! [X50,X51,X52] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X52)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X51),X50),c_HOL_Ozero__class_Ozero(X52),X52)
| ~ c_HOL_Oord__class_Oless(X50,c_HOL_Ozero__class_Ozero(X52),X52)
| ~ c_HOL_Oord__class_Oless(X51,c_HOL_Ozero__class_Ozero(X52),X52) ),
inference(variable_rename,[status(thm)],[c_0_290]) ).
fof(c_0_486_487,plain,
! [X50,X51,X52] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X52)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X52),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X51),X50),X52)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X52),X50,X52)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X52),X51,X52) ),
inference(variable_rename,[status(thm)],[c_0_291]) ).
fof(c_0_487_488,plain,
! [X51,X52,X53,X54] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51),X54)
| ~ c_HOL_Oord__class_Oless(X53,X52,X54) ),
inference(variable_rename,[status(thm)],[c_0_292]) ).
fof(c_0_488_489,plain,
! [X51,X52,X53,X54] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51),X54)
| ~ c_HOL_Oord__class_Oless(X53,X52,X54) ),
inference(variable_rename,[status(thm)],[c_0_293]) ).
fof(c_0_489_490,plain,
! [X51,X52,X53,X54] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X52),X54)
| ~ c_HOL_Oord__class_Oless(X53,X52,X54) ),
inference(variable_rename,[status(thm)],[c_0_294]) ).
fof(c_0_490,plain,
! [X51,X52,X53,X54] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X52),X54)
| ~ c_HOL_Oord__class_Oless(X53,X52,X54) ),
inference(variable_rename,[status(thm)],[c_0_295]) ).
fof(c_0_491,plain,
! [X14,X15,X16] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X15,X16)),c_Lambda_Olift(X14,X16)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X15),X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_296])])]) ).
fof(c_0_492,plain,
! [X51,X52,X53,X54] :
( ~ class_Ring__and__Field_Oordered__semidom(X54)
| c_HOL_Oord__class_Oless(X52,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51),X54)
| ~ c_HOL_Oord__class_Oless(X52,X51,X54)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X54),X53,X54) ),
inference(variable_rename,[status(thm)],[c_0_297]) ).
fof(c_0_493,plain,
! [X63,X64,X65,X66] :
( c_List_Olistsp(X65,c_List_Oappend(X64,X63,X66),X66)
| ~ c_List_Olistsp(X65,X63,X66)
| ~ c_List_Olistsp(X65,X64,X66) ),
inference(variable_rename,[status(thm)],[c_0_298]) ).
fof(c_0_494,plain,
! [X44,X45] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X45)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X45),X44,X45)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),X44),X45) ),
inference(variable_rename,[status(thm)],[c_0_299]) ).
fof(c_0_495,plain,
! [X44,X45] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X45)
| c_HOL_Oord__class_Oless(X44,c_HOL_Ozero__class_Ozero(X45),X45)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),X44),c_HOL_Ozero__class_Ozero(X45),X45) ),
inference(variable_rename,[status(thm)],[c_0_300]) ).
fof(c_0_496,plain,
! [X44,X45] :
( ~ class_Ring__and__Field_Oordered__idom(X45)
| c_HOL_Oord__class_Oless(X44,c_HOL_Ozero__class_Ozero(X45),X45)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),X44),c_HOL_Ozero__class_Ozero(X45),X45) ),
inference(variable_rename,[status(thm)],[c_0_301]) ).
fof(c_0_497,plain,
! [X56,X57,X58,X59] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X59)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X58),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X57),X56)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X57),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X59),X58),X56)) ),
inference(variable_rename,[status(thm)],[c_0_302]) ).
fof(c_0_498,plain,
! [X51,X52,X53,X54] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X54)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X51)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51)) ),
inference(variable_rename,[status(thm)],[c_0_303]) ).
fof(c_0_499,plain,
! [X46,X47,X48,X49] :
( ~ class_OrderedGroup_Oab__group__add(X49)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),X46)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X47),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46)) ),
inference(variable_rename,[status(thm)],[c_0_304]) ).
fof(c_0_500,plain,
! [X46,X47,X48,X49] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X48,X49),X47),X46))
| ~ hBOOL(hAPP(hAPP(X48,X47),X46)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_305])])]) ).
fof(c_0_501,plain,
! [X63,X64,X65,X66] :
( c_List_Olistsp(X65,X63,X66)
| ~ c_List_Olistsp(X65,c_List_Oappend(X64,X63,X66),X66) ),
inference(variable_rename,[status(thm)],[c_0_306]) ).
fof(c_0_502,plain,
! [X63,X64,X65,X66] :
( c_List_Olistsp(X65,X64,X66)
| ~ c_List_Olistsp(X65,c_List_Oappend(X64,X63,X66),X66) ),
inference(variable_rename,[status(thm)],[c_0_307]) ).
fof(c_0_503,plain,
! [X27,X28,X29] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X27,c_Lambda_OdB_OVar(X29),X28)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X27)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_308])])]) ).
fof(c_0_504,plain,
! [X46,X47,X48,X49] :
( c_Wellfounded_Oaccp(X47,X46,X49)
| ~ hBOOL(hAPP(hAPP(X47,X46),X48))
| ~ c_Wellfounded_Oaccp(X47,X48,X49) ),
inference(variable_rename,[status(thm)],[c_0_309]) ).
fof(c_0_505,plain,
! [X50,X51,X52,X53] :
( c_Wellfounded_Oaccp(X50,X52,X53)
| ~ hBOOL(hAPP(hAPP(X50,X52),X51))
| ~ c_Wellfounded_Oaccp(X50,X51,X53) ),
inference(variable_rename,[status(thm)],[c_0_310]) ).
fof(c_0_506,plain,
! [X44,X45] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X45)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X45),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),X44),X45)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X45),X44,X45) ),
inference(variable_rename,[status(thm)],[c_0_311]) ).
fof(c_0_507,plain,
! [X44,X45] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X45)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),X44),c_HOL_Ozero__class_Ozero(X45),X45)
| ~ c_HOL_Oord__class_Oless(X44,c_HOL_Ozero__class_Ozero(X45),X45) ),
inference(variable_rename,[status(thm)],[c_0_312]) ).
fof(c_0_508,plain,
! [X44,X45] :
( ~ class_Ring__and__Field_Oordered__idom(X45)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),X44),c_HOL_Ozero__class_Ozero(X45),X45)
| ~ c_HOL_Oord__class_Oless(X44,c_HOL_Ozero__class_Ozero(X45),X45) ),
inference(variable_rename,[status(thm)],[c_0_313]) ).
fof(c_0_509,plain,
! [X14] :
( hBOOL(hAPP(c_InductTermi_OIT,X14))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X14,tc_Lambda_OdB) ),
inference(variable_rename,[status(thm)],[c_0_314]) ).
fof(c_0_510,plain,
! [X16,X17,X18,X19] :
( c_Type_Otyping(X18,X16,X19)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X17),X16))
| ~ c_Type_Otyping(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_315]) ).
fof(c_0_511,plain,
! [X9,X10] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X9),c_Lambda_OdB_OVar(X10))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X9)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_316])])]) ).
fof(c_0_512,plain,
! [X46,X47,X48,X49] :
( ~ class_Orderings_Opreorder(X49)
| c_HOL_Oord__class_Oless(X48,X46,X49)
| ~ c_HOL_Oord__class_Oless(X47,X46,X49)
| ~ c_HOL_Oord__class_Oless(X48,X47,X49) ),
inference(variable_rename,[status(thm)],[c_0_317]) ).
fof(c_0_513,plain,
! [X46,X47,X48,X49] :
( ~ class_Orderings_Oorder(X49)
| c_HOL_Oord__class_Oless(X46,X48,X49)
| ~ c_HOL_Oord__class_Oless(X46,X47,X49)
| ~ c_HOL_Oord__class_Oless(X47,X48,X49) ),
inference(variable_rename,[status(thm)],[c_0_318]) ).
fof(c_0_514,plain,
! [X13,X14] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X14)),c_Lambda_OdB_OAbs(X13)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X14),X13)) ),
inference(variable_rename,[status(thm)],[c_0_319]) ).
fof(c_0_515,plain,
! [X22,X23,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X24)
| c_HOL_Oord__class_Oless(X23,X22,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X23,X24),c_Nat_Osemiring__1__class_Oof__nat(X22,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_320]) ).
fof(c_0_516,plain,
! [X21,X22] :
( ~ class_Ring__and__Field_Oordered__semidom(X22)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X22),c_Nat_Osemiring__1__class_Oof__nat(X21,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_321]) ).
fof(c_0_517,plain,
! [X22,X23,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X24)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X23,X24),c_Nat_Osemiring__1__class_Oof__nat(X22,X24),X24)
| ~ c_HOL_Oord__class_Oless(X23,X22,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_322]) ).
fof(c_0_518,plain,
! [X8] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X8,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X8)) ),
inference(variable_rename,[status(thm)],[c_0_323]) ).
fof(c_0_519,plain,
! [X49,X50,X51] :
( hBOOL(hAPP(hAPP(X51,X49),X50))
| c_HOL_Oord__class_Oless(X49,X50,tc_nat)
| X50 = X49
| c_HOL_Oord__class_Oless(X50,X49,tc_nat) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_324])])]) ).
fof(c_0_520,plain,
! [X21,X22] :
( ~ class_Ring__and__Field_Oordered__semidom(X22)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X22),c_Nat_Osemiring__1__class_Oof__nat(X21,X22),X22)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_325]) ).
fof(c_0_521,plain,
! [X46,X47,X48,X49] :
( ~ class_Ring__and__Field_Oidom(X49)
| ~ class_Int_Onumber__ring(X49)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X47) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X49),X48),X46)
| X47 = X46 ),
inference(variable_rename,[status(thm)],[c_0_326]) ).
fof(c_0_522,plain,
! [X50,X51,X52] :
( ~ class_Orderings_Opreorder(X52)
| ~ c_HOL_Oord__class_Oless(X50,X51,X52)
| ~ c_HOL_Oord__class_Oless(X51,X50,X52) ),
inference(variable_rename,[status(thm)],[c_0_327]) ).
fof(c_0_523,plain,
! [X46,X47,X48] :
( ~ class_Orderings_Opreorder(X48)
| ~ c_HOL_Oord__class_Oless(X46,X47,X48)
| ~ c_HOL_Oord__class_Oless(X47,X46,X48) ),
inference(variable_rename,[status(thm)],[c_0_328]) ).
fof(c_0_524,plain,
! [X46,X47,X48] :
( ~ class_Orderings_Olinorder(X48)
| ~ c_HOL_Oord__class_Oless(X47,X46,X48)
| ~ c_HOL_Oord__class_Oless(X46,X47,X48) ),
inference(variable_rename,[status(thm)],[c_0_329]) ).
fof(c_0_525,plain,
! [X50,X51,X52] :
( ~ class_Orderings_Oorder(X52)
| ~ c_HOL_Oord__class_Oless(X51,X50,X52)
| ~ c_HOL_Oord__class_Oless(X50,X51,X52) ),
inference(variable_rename,[status(thm)],[c_0_330]) ).
fof(c_0_526,plain,
! [X58,X59,X60,X61] :
( c_List_Oappend(X60,X59,X61) != c_List_Oappend(X60,X58,X61)
| X59 = X58 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_331])])]) ).
fof(c_0_527,plain,
! [X58,X59,X60,X61] :
( c_List_Oappend(X59,X60,X61) != c_List_Oappend(X58,X60,X61)
| X59 = X58 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_332])])]) ).
fof(c_0_528,plain,
! [X51,X52,X53,X54] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X54)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X52),X53) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X51),X53)
| X52 = X51 ),
inference(variable_rename,[status(thm)],[c_0_333]) ).
fof(c_0_529,plain,
! [X51,X52,X53,X54] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X54)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X52) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51)
| X52 = X51 ),
inference(variable_rename,[status(thm)],[c_0_334]) ).
fof(c_0_530,plain,
! [X51,X52,X53,X54] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X54)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X52) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X54),X53),X51)
| X52 = X51 ),
inference(variable_rename,[status(thm)],[c_0_335]) ).
fof(c_0_531,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_336])])]) ).
fof(c_0_532,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_337])])]) ).
fof(c_0_533,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_338])])]) ).
fof(c_0_534,plain,
! [X27,X28,X29] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X28),X27,X29) = c_Lambda_OdB_OVar(X28)
| ~ c_HOL_Oord__class_Oless(X28,X29,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_339]) ).
fof(c_0_535,plain,
! [X22,X23] :
( ~ class_Ring__and__Field_Oordered__semidom(X23)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X22,X23),c_HOL_Ozero__class_Ozero(X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_340]) ).
fof(c_0_536,plain,
! [X9,X10] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X9,X10)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X9)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_341])])]) ).
fof(c_0_537,plain,
! [X39,X40,X41] :
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X41),X39,X40) = c_Lambda_OdB_OVar(X41)
| X41 = X40
| c_HOL_Oord__class_Oless(X40,X41,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_342]) ).
fof(c_0_538,plain,
! [X46,X47,X48] :
( ~ class_Orderings_Olinorder(X48)
| X47 = X46
| c_HOL_Oord__class_Oless(X47,X46,X48)
| c_HOL_Oord__class_Oless(X46,X47,X48) ),
inference(variable_rename,[status(thm)],[c_0_343]) ).
fof(c_0_539,plain,
! [X46,X47,X48] :
( ~ class_Orderings_Olinorder(X48)
| c_HOL_Oord__class_Oless(X46,X47,X48)
| X47 = X46
| c_HOL_Oord__class_Oless(X47,X46,X48) ),
inference(variable_rename,[status(thm)],[c_0_344]) ).
fof(c_0_540,plain,
! [X46,X47,X48] :
( ~ class_Orderings_Olinorder(X48)
| c_HOL_Oord__class_Oless(X46,X47,X48)
| c_HOL_Oord__class_Oless(X47,X46,X48)
| X47 = X46 ),
inference(variable_rename,[status(thm)],[c_0_345]) ).
fof(c_0_541,plain,
! [X46,X47,X48] :
( ~ class_Orderings_Olinorder(X48)
| X47 = X46
| c_HOL_Oord__class_Oless(X46,X47,X48)
| c_HOL_Oord__class_Oless(X47,X46,X48) ),
inference(variable_rename,[status(thm)],[c_0_346]) ).
fof(c_0_542,plain,
! [X46,X47,X48] :
( ~ class_Ring__and__Field_Oordered__idom(X48)
| c_HOL_Oord__class_Oless(X46,X47,X48)
| c_HOL_Oord__class_Oless(X47,X46,X48)
| X47 = X46 ),
inference(variable_rename,[status(thm)],[c_0_347]) ).
fof(c_0_543,plain,
! [X35,X36,X37,X38] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X38),X36) != hAPP(hAPP(c_Lambda_OdB_OApp,X37),X35)
| X36 = X35 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_348])])]) ).
fof(c_0_544,plain,
! [X35,X36,X37,X38] :
( hAPP(hAPP(c_Lambda_OdB_OApp,X38),X36) != hAPP(hAPP(c_Lambda_OdB_OApp,X37),X35)
| X38 = X37 ),
inference(variable_rename,[status(thm)],[c_0_349]) ).
fof(c_0_545,plain,
! [X26,X27,X28,X29] :
( hAPP(hAPP(c_Type_Otype_OFun,X29),X27) != hAPP(hAPP(c_Type_Otype_OFun,X28),X26)
| X27 = X26 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_350])])]) ).
fof(c_0_546,plain,
! [X26,X27,X28,X29] :
( hAPP(hAPP(c_Type_Otype_OFun,X29),X27) != hAPP(hAPP(c_Type_Otype_OFun,X28),X26)
| X29 = X28 ),
inference(variable_rename,[status(thm)],[c_0_351]) ).
fof(c_0_547,plain,
! [X41,X42] :
( c_HOL_Oord__class_Oless(X41,X41,tc_nat)
| c_Lambda_Osubst(c_Lambda_OdB_OVar(X41),X42,X41) = X42 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_352])])]) ).
fof(c_0_548,plain,
! [X51,X52,X53] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X53)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X53),X52),X51) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X53),X51),X52) ),
inference(variable_rename,[status(thm)],[c_0_353]) ).
fof(c_0_549,plain,
! [X50,X51,X52] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X52)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X51),X50) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X52),X50),X51) ),
inference(variable_rename,[status(thm)],[c_0_354]) ).
fof(c_0_550,plain,
! [X46,X47,X48] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X48)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X47),X46) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X48),X46),X47) ),
inference(variable_rename,[status(thm)],[c_0_355]) ).
fof(c_0_551,plain,
! [X15,X16,X17] :
( hAPP(X16,X15) = X17
| ~ c_Type_Otyping(X16,c_Lambda_OdB_OVar(X15),X17) ),
inference(variable_rename,[status(thm)],[c_0_356]) ).
fof(c_0_552,plain,
! [X46,X47] :
( c_HOL_Oord__class_Oless(X46,X47,tc_nat)
| c_HOL_Oord__class_Oless(X47,X46,tc_nat)
| X47 = X46 ),
inference(variable_rename,[status(thm)],[c_0_357]) ).
fof(c_0_553,plain,
! [X22,X23] :
( c_HOL_Oord__class_Oless(X22,X23,tc_nat)
| c_HOL_Oord__class_Oless(X23,X22,tc_nat)
| X23 = X22 ),
inference(variable_rename,[status(thm)],[c_0_358]) ).
fof(c_0_554,plain,
! [X39,X40] :
( c_Lambda_Olift(c_Lambda_OdB_OVar(X40),X39) = c_Lambda_OdB_OVar(X40)
| ~ c_HOL_Oord__class_Oless(X40,X39,tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_359]) ).
fof(c_0_555,plain,
! [X44,X45,X46] :
( ~ class_Ring__and__Field_Oidom(X46)
| ~ class_Int_Onumber__ring(X46)
| X44 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X46),X44),X45)
| X45 = c_HOL_Ozero__class_Ozero(X46) ),
inference(variable_rename,[status(thm)],[c_0_360]) ).
fof(c_0_556,plain,
! [X44,X45] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X45)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),X44) != c_HOL_Ozero__class_Ozero(X45)
| X44 = c_HOL_Ozero__class_Ozero(X45) ),
inference(variable_rename,[status(thm)],[c_0_361]) ).
fof(c_0_557,plain,
! [X52,X53,X54] :
( c_List_Oappend(X53,X52,X54) != c_List_Olist_ONil(X54)
| X52 = c_List_Olist_ONil(X54) ),
inference(variable_rename,[status(thm)],[c_0_362]) ).
fof(c_0_558,plain,
! [X52,X53,X54] :
( c_List_Oappend(X53,X52,X54) != c_List_Olist_ONil(X54)
| X53 = c_List_Olist_ONil(X54) ),
inference(variable_rename,[status(thm)],[c_0_363]) ).
fof(c_0_559,plain,
! [X52,X53,X54] :
( c_List_Olist_ONil(X54) != c_List_Oappend(X53,X52,X54)
| X52 = c_List_Olist_ONil(X54) ),
inference(variable_rename,[status(thm)],[c_0_364]) ).
fof(c_0_560,plain,
! [X52,X53,X54] :
( c_List_Olist_ONil(X54) != c_List_Oappend(X53,X52,X54)
| X53 = c_List_Olist_ONil(X54) ),
inference(variable_rename,[status(thm)],[c_0_365]) ).
fof(c_0_561,plain,
! [X41,X42] :
( ~ class_Orderings_Opreorder(X42)
| ~ c_HOL_Oord__class_Oless(X41,X41,X42) ),
inference(variable_rename,[status(thm)],[c_0_366]) ).
fof(c_0_562,plain,
! [X41,X42] :
( ~ class_Orderings_Olinorder(X42)
| ~ c_HOL_Oord__class_Oless(X41,X41,X42) ),
inference(variable_rename,[status(thm)],[c_0_367]) ).
fof(c_0_563,plain,
! [X41,X42] :
( ~ class_Orderings_Oorder(X42)
| ~ c_HOL_Oord__class_Oless(X41,X41,X42) ),
inference(variable_rename,[status(thm)],[c_0_368]) ).
fof(c_0_564,plain,
! [X52,X53,X54] :
( X52 != c_List_Oappend(X53,X52,X54)
| X53 = c_List_Olist_ONil(X54) ),
inference(variable_rename,[status(thm)],[c_0_369]) ).
fof(c_0_565,plain,
! [X52,X53,X54] :
( c_List_Oappend(X53,X52,X54) != X52
| X53 = c_List_Olist_ONil(X54) ),
inference(variable_rename,[status(thm)],[c_0_370]) ).
fof(c_0_566,plain,
! [X52,X53,X54] :
( X53 != c_List_Oappend(X53,X52,X54)
| X52 = c_List_Olist_ONil(X54) ),
inference(variable_rename,[status(thm)],[c_0_371]) ).
fof(c_0_567,plain,
! [X52,X53,X54] :
( c_List_Oappend(X53,X52,X54) != X53
| X52 = c_List_Olist_ONil(X54) ),
inference(variable_rename,[status(thm)],[c_0_372]) ).
fof(c_0_568,plain,
! [X14] :
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X14)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X14)) ),
inference(variable_rename,[status(thm)],[c_0_373]) ).
fof(c_0_569,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_374]) ).
fof(c_0_570,plain,
! [X41,X42] :
( ~ class_Ring__and__Field_Oidom(X42)
| ~ class_Int_Onumber__ring(X42)
| X41 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X42),X41),c_HOL_Ozero__class_Ozero(X42)) ),
inference(variable_rename,[status(thm)],[c_0_375]) ).
fof(c_0_571,plain,
! [X44,X45] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),c_HOL_Ozero__class_Ozero(X45)),X44) = X44 ),
inference(variable_rename,[status(thm)],[c_0_376]) ).
fof(c_0_572,plain,
! [X44,X45] :
( ~ class_OrderedGroup_Omonoid__add(X45)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),c_HOL_Ozero__class_Ozero(X45)),X44) = X44 ),
inference(variable_rename,[status(thm)],[c_0_377]) ).
fof(c_0_573,plain,
! [X44,X45] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X45)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),c_HOL_Ozero__class_Ozero(X45)),X44) = X44 ),
inference(variable_rename,[status(thm)],[c_0_378]) ).
fof(c_0_574,plain,
! [X41,X42] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X42)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X42),c_HOL_Ozero__class_Ozero(X42)),X41) = X41 ),
inference(variable_rename,[status(thm)],[c_0_379]) ).
fof(c_0_575,plain,
! [X44,X45] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),c_HOL_Ozero__class_Ozero(X45)) = X44 ),
inference(variable_rename,[status(thm)],[c_0_380]) ).
fof(c_0_576,plain,
! [X44,X45] :
( ~ class_OrderedGroup_Omonoid__add(X45)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),c_HOL_Ozero__class_Ozero(X45)) = X44 ),
inference(variable_rename,[status(thm)],[c_0_381]) ).
fof(c_0_577,plain,
! [X44,X45] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X45)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X45),X44),c_HOL_Ozero__class_Ozero(X45)) = X44 ),
inference(variable_rename,[status(thm)],[c_0_382]) ).
fof(c_0_578,plain,
! [X21] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X21,tc_nat)
| X21 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(variable_rename,[status(thm)],[c_0_383]) ).
fof(c_0_579,plain,
! [X22,X23,X24] :
( ~ class_Nat_Osemiring__char__0(X24)
| c_Nat_Osemiring__1__class_Oof__nat(X23,X24) != c_Nat_Osemiring__1__class_Oof__nat(X22,X24)
| X23 = X22 ),
inference(variable_rename,[status(thm)],[c_0_384]) ).
fof(c_0_580,plain,
! [X6,X7] :
( class_Orderings_Opreorder(tc_fun(X6,X7))
| ~ class_Orderings_Opreorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_385]) ).
fof(c_0_581,plain,
! [X6,X7] :
( class_Orderings_Oorder(tc_fun(X6,X7))
| ~ class_Orderings_Oorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_386]) ).
fof(c_0_582,plain,
! [X4] :
( ~ class_Ring__and__Field_Osemiring__1(X4)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_387]) ).
fof(c_0_583,plain,
! [X48,X49] :
( c_Lambda_OdB_OAbs(X49) != c_Lambda_OdB_OAbs(X48)
| X49 = X48 ),
inference(variable_rename,[status(thm)],[c_0_388]) ).
fof(c_0_584,plain,
! [X18,X19] :
( c_Lambda_OdB_OVar(X19) != c_Lambda_OdB_OVar(X18)
| X19 = X18 ),
inference(variable_rename,[status(thm)],[c_0_389]) ).
cnf(c_0_585,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_390]) ).
cnf(c_0_586,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_391]) ).
cnf(c_0_587,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_392]) ).
cnf(c_0_588,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_393]) ).
cnf(c_0_589,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_394]) ).
cnf(c_0_590,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_395]) ).
cnf(c_0_591,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_396]) ).
cnf(c_0_592,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_397]) ).
cnf(c_0_593,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_398]) ).
cnf(c_0_594,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_399]) ).
cnf(c_0_595,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_400]) ).
cnf(c_0_596,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_401]) ).
cnf(c_0_597,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_402]) ).
cnf(c_0_598,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_403]) ).
cnf(c_0_599,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_404]) ).
cnf(c_0_600,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_405]) ).
cnf(c_0_601,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_406]) ).
cnf(c_0_602,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_407]) ).
cnf(c_0_603,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_408]) ).
cnf(c_0_604,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_409]) ).
cnf(c_0_605,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_410]) ).
cnf(c_0_606,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_411]) ).
cnf(c_0_607,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_412]) ).
cnf(c_0_608,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_413]) ).
cnf(c_0_609,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_414]) ).
cnf(c_0_610,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_415]) ).
cnf(c_0_611,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_416]) ).
cnf(c_0_612,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_417]) ).
cnf(c_0_613,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_418]) ).
cnf(c_0_614,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_419]) ).
cnf(c_0_615,plain,
( c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_420]) ).
cnf(c_0_616,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_421]) ).
cnf(c_0_617,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_422]) ).
cnf(c_0_618,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_423]) ).
cnf(c_0_619,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_424]) ).
cnf(c_0_620,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_425]) ).
cnf(c_0_621,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_426]) ).
cnf(c_0_622,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_427]) ).
cnf(c_0_623,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_428]) ).
cnf(c_0_624,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_429]) ).
cnf(c_0_625,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_430]) ).
cnf(c_0_626,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_431]) ).
cnf(c_0_627,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_432]) ).
cnf(c_0_628,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_433]) ).
cnf(c_0_629,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X4),X7) ),
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_630,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X7),X4) ),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_631,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_436]) ).
cnf(c_0_632,plain,
( c_Type_Otyping(X1,c_Lambda_Osubst(X2,X3,X4),X5)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
inference(split_conjunct,[status(thm)],[c_0_437]) ).
cnf(c_0_633,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_438]) ).
cnf(c_0_634,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_439]) ).
cnf(c_0_635,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_440]) ).
cnf(c_0_636,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_441]) ).
cnf(c_0_637,plain,
( c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),hAPP(hAPP(c_Type_Otype_OFun,X2),X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_638,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_443]) ).
cnf(c_0_639,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_444]) ).
cnf(c_0_640,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_445]) ).
cnf(c_0_641,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_446]) ).
cnf(c_0_642,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_447]) ).
cnf(c_0_643,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_448]) ).
cnf(c_0_644,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_449]) ).
cnf(c_0_645,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_450]) ).
cnf(c_0_646,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_451]) ).
cnf(c_0_647,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_452]) ).
cnf(c_0_648,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_453]) ).
cnf(c_0_649,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_454]) ).
cnf(c_0_650,plain,
( c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_651,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_456]) ).
cnf(c_0_652,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_457]) ).
cnf(c_0_653,plain,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_Lambda_Olift(X2,X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_654,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_459]) ).
cnf(c_0_655,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_460]) ).
cnf(c_0_656,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_461]) ).
cnf(c_0_657,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_462]) ).
cnf(c_0_658,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_463]) ).
cnf(c_0_659,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_464]) ).
cnf(c_0_660,plain,
( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_661,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_466]) ).
cnf(c_0_662,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_467]) ).
cnf(c_0_663,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_468]) ).
cnf(c_0_664,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_469]) ).
cnf(c_0_665,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_470]) ).
cnf(c_0_666,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_471]) ).
cnf(c_0_667,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_472]) ).
cnf(c_0_668,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_473]) ).
cnf(c_0_669,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_474]) ).
cnf(c_0_670,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_475]) ).
cnf(c_0_671,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_476]) ).
cnf(c_0_672,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_477]) ).
cnf(c_0_673,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_478]) ).
cnf(c_0_674,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_479]) ).
cnf(c_0_675,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_480]) ).
cnf(c_0_676,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_481]) ).
cnf(c_0_677,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_482]) ).
cnf(c_0_678,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_483]) ).
cnf(c_0_679,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_484]) ).
cnf(c_0_680,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_485]) ).
cnf(c_0_681,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_486]) ).
cnf(c_0_682,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_487]) ).
cnf(c_0_683,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_488]) ).
cnf(c_0_684,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_489]) ).
cnf(c_0_685,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_490]) ).
cnf(c_0_686,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_491]) ).
cnf(c_0_687,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_492]) ).
cnf(c_0_688,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_493]) ).
cnf(c_0_689,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_494]) ).
cnf(c_0_690,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_495]) ).
cnf(c_0_691,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_496]) ).
cnf(c_0_692,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_497]) ).
cnf(c_0_693,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_498]) ).
cnf(c_0_694,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_499]) ).
cnf(c_0_695,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_500]) ).
cnf(c_0_696,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_501]) ).
cnf(c_0_697,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_502]) ).
cnf(c_0_698,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_503]) ).
cnf(c_0_699,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_504]) ).
cnf(c_0_700,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_505]) ).
cnf(c_0_701,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_506]) ).
cnf(c_0_702,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_507]) ).
cnf(c_0_703,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_508]) ).
cnf(c_0_704,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_509]) ).
cnf(c_0_705,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_510]) ).
cnf(c_0_706,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_511]) ).
cnf(c_0_707,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_512]) ).
cnf(c_0_708,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_513]) ).
cnf(c_0_709,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_514]) ).
cnf(c_0_710,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_515]) ).
cnf(c_0_711,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_516]) ).
cnf(c_0_712,plain,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_517]) ).
cnf(c_0_713,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_518]) ).
cnf(c_0_714,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_519]) ).
cnf(c_0_715,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_520]) ).
cnf(c_0_716,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_521]) ).
cnf(c_0_717,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_522]) ).
cnf(c_0_718,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_523]) ).
cnf(c_0_719,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_524]) ).
cnf(c_0_720,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_525]) ).
cnf(c_0_721,plain,
( X1 = X2
| c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_526]) ).
cnf(c_0_722,plain,
( X1 = X2
| c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_527]) ).
cnf(c_0_723,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_528]) ).
cnf(c_0_724,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_529]) ).
cnf(c_0_725,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_530]) ).
cnf(c_0_726,plain,
( X1 = X2
| c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_531]) ).
cnf(c_0_727,plain,
( X1 = X2
| c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_532]) ).
cnf(c_0_728,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_533]) ).
cnf(c_0_729,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_534]) ).
cnf(c_0_730,plain,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_535]) ).
cnf(c_0_731,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_536]) ).
cnf(c_0_732,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_537]) ).
cnf(c_0_733,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_538]) ).
cnf(c_0_734,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_539]) ).
cnf(c_0_735,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_540]) ).
cnf(c_0_736,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_541]) ).
cnf(c_0_737,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_542]) ).
cnf(c_0_738,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_543]) ).
cnf(c_0_739,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_544]) ).
cnf(c_0_740,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_545]) ).
cnf(c_0_741,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_546]) ).
cnf(c_0_742,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_547]) ).
cnf(c_0_743,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_548]) ).
cnf(c_0_744,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_549]) ).
cnf(c_0_745,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_550]) ).
cnf(c_0_746,plain,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_551]) ).
cnf(c_0_747,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_552]) ).
cnf(c_0_748,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_553]) ).
cnf(c_0_749,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_554]) ).
cnf(c_0_750,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_555]) ).
cnf(c_0_751,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_556]) ).
cnf(c_0_752,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_557]) ).
cnf(c_0_753,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_558]) ).
cnf(c_0_754,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_559]) ).
cnf(c_0_755,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_560]) ).
cnf(c_0_756,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_561]) ).
cnf(c_0_757,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_562]) ).
cnf(c_0_758,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_563]) ).
cnf(c_0_759,plain,
( X1 = c_List_Olist_ONil(X2)
| X3 != c_List_Oappend(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_564]) ).
cnf(c_0_760,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_565]) ).
cnf(c_0_761,plain,
( X1 = c_List_Olist_ONil(X2)
| X3 != c_List_Oappend(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_566]) ).
cnf(c_0_762,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_567]) ).
cnf(c_0_763,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_568]) ).
cnf(c_0_764,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_569]) ).
cnf(c_0_765,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_570]) ).
cnf(c_0_766,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_571]) ).
cnf(c_0_767,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_572]) ).
cnf(c_0_768,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_573]) ).
cnf(c_0_769,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_574]) ).
cnf(c_0_770,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_575]) ).
cnf(c_0_771,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_576]) ).
cnf(c_0_772,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_577]) ).
cnf(c_0_773,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_578]) ).
cnf(c_0_774,plain,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| ~ class_Nat_Osemiring__char__0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_579]) ).
cnf(c_0_775,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_776,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_581]) ).
cnf(c_0_777,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_778,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(split_conjunct,[status(thm)],[c_0_583]) ).
cnf(c_0_779,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_780,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_585,
[final] ).
cnf(c_0_781,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_586,
[final] ).
cnf(c_0_782,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_587,
[final] ).
cnf(c_0_783,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_588,
[final] ).
cnf(c_0_784,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_589,
[final] ).
cnf(c_0_785,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_590,
[final] ).
cnf(c_0_786,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_591,
[final] ).
cnf(c_0_787,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_592,
[final] ).
cnf(c_0_788,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_593,
[final] ).
cnf(c_0_789,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_594,
[final] ).
cnf(c_0_790,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_595,
[final] ).
cnf(c_0_791,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_596,
[final] ).
cnf(c_0_792,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_597,
[final] ).
cnf(c_0_793,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_598,
[final] ).
cnf(c_0_794,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_599,
[final] ).
cnf(c_0_795,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_600,
[final] ).
cnf(c_0_796,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_601,
[final] ).
cnf(c_0_797,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_602,
[final] ).
cnf(c_0_798,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_603,
[final] ).
cnf(c_0_799,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_604,
[final] ).
cnf(c_0_800,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_605,
[final] ).
cnf(c_0_801,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_606,
[final] ).
cnf(c_0_802,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_607,
[final] ).
cnf(c_0_803,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_608,
[final] ).
cnf(c_0_804,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_609,
[final] ).
cnf(c_0_805,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_610,
[final] ).
cnf(c_0_806,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_611,
[final] ).
cnf(c_0_807,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_612,
[final] ).
cnf(c_0_808,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_613,
[final] ).
cnf(c_0_809,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_614,
[final] ).
cnf(c_0_810,plain,
( c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
c_0_615,
[final] ).
cnf(c_0_811,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_616,
[final] ).
cnf(c_0_812,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_617,
[final] ).
cnf(c_0_813,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_618,
[final] ).
cnf(c_0_814,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_619,
[final] ).
cnf(c_0_815,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_620,
[final] ).
cnf(c_0_816,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_621,
[final] ).
cnf(c_0_817,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_622,
[final] ).
cnf(c_0_818,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_623,
[final] ).
cnf(c_0_819,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_624,
[final] ).
cnf(c_0_820,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_625,
[final] ).
cnf(c_0_821,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_626,
[final] ).
cnf(c_0_822,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_627,
[final] ).
cnf(c_0_823,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_628,
[final] ).
cnf(c_0_824,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
c_0_629,
[final] ).
cnf(c_0_825,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
c_0_630,
[final] ).
cnf(c_0_826,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_631,
[final] ).
cnf(c_0_827,plain,
( c_Type_Otyping(X1,c_Lambda_Osubst(X2,X3,X4),X5)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
c_0_632,
[final] ).
cnf(c_0_828,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_633,
[final] ).
cnf(c_0_829,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_634,
[final] ).
cnf(c_0_830,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_635,
[final] ).
cnf(c_0_831,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_636,
[final] ).
cnf(c_0_832,plain,
( c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),hAPP(hAPP(c_Type_Otype_OFun,X2),X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X3,X4) ),
c_0_637,
[final] ).
cnf(c_0_833,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_638,
[final] ).
cnf(c_0_834,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_639,
[final] ).
cnf(c_0_835,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
c_0_640,
[final] ).
cnf(c_0_836,plain,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
c_0_641,
[final] ).
cnf(c_0_837,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_642,
[final] ).
cnf(c_0_838,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_643,
[final] ).
cnf(c_0_839,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_644,
[final] ).
cnf(c_0_840,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_645,
[final] ).
cnf(c_0_841,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_646,
[final] ).
cnf(c_0_842,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_647,
[final] ).
cnf(c_0_843,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_648,
[final] ).
cnf(c_0_844,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_649,
[final] ).
cnf(c_0_845,plain,
( c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
c_0_650,
[final] ).
cnf(c_0_846,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_651,
[final] ).
cnf(c_0_847,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_652,
[final] ).
cnf(c_0_848,plain,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_Lambda_Olift(X2,X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
c_0_653,
[final] ).
cnf(c_0_849,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_654,
[final] ).
cnf(c_0_850,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X4,X5),X3),X2))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_655,
[final] ).
cnf(c_0_851,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_656,
[final] ).
cnf(c_0_852,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_657,
[final] ).
cnf(c_0_853,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_658,
[final] ).
cnf(c_0_854,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_659,
[final] ).
cnf(c_0_855,plain,
( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
c_0_660,
[final] ).
cnf(c_0_856,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_661,
[final] ).
cnf(c_0_857,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_662,
[final] ).
cnf(c_0_858,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_663,
[final] ).
cnf(c_0_859,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_664,
[final] ).
cnf(c_0_860,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_665,
[final] ).
cnf(c_0_861,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_666,
[final] ).
cnf(c_0_862,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_667,
[final] ).
cnf(c_0_863,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_668,
[final] ).
cnf(c_0_864,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_669,
[final] ).
cnf(c_0_865,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_670,
[final] ).
cnf(c_0_866,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_671,
[final] ).
cnf(c_0_867,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_672,
[final] ).
cnf(c_0_868,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_673,
[final] ).
cnf(c_0_869,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_674,
[final] ).
cnf(c_0_870,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_675,
[final] ).
cnf(c_0_871,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_676,
[final] ).
cnf(c_0_872,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_677,
[final] ).
cnf(c_0_873,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_678,
[final] ).
cnf(c_0_874,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_679,
[final] ).
cnf(c_0_875,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_680,
[final] ).
cnf(c_0_876,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_681,
[final] ).
cnf(c_0_877,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_682,
[final] ).
cnf(c_0_878,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_683,
[final] ).
cnf(c_0_879,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_684,
[final] ).
cnf(c_0_880,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_685,
[final] ).
cnf(c_0_881,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_686,
[final] ).
cnf(c_0_882,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_687,
[final] ).
cnf(c_0_883,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_688,
[final] ).
cnf(c_0_884,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_689,
[final] ).
cnf(c_0_885,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_690,
[final] ).
cnf(c_0_886,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_691,
[final] ).
cnf(c_0_887,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_692,
[final] ).
cnf(c_0_888,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_693,
[final] ).
cnf(c_0_889,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_694,
[final] ).
cnf(c_0_890,plain,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X4),X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
c_0_695,
[final] ).
cnf(c_0_891,plain,
( c_List_Olistsp(X1,X3,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
c_0_696,
[final] ).
cnf(c_0_892,plain,
( c_List_Olistsp(X1,X2,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
c_0_697,
[final] ).
cnf(c_0_893,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,c_Lambda_OdB_OVar(X2),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_698,
[final] ).
cnf(c_0_894,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
c_0_699,
[final] ).
cnf(c_0_895,plain,
( c_Wellfounded_Oaccp(X1,X4,X3)
| ~ c_Wellfounded_Oaccp(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
c_0_700,
[final] ).
cnf(c_0_896,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_701,
[final] ).
cnf(c_0_897,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_702,
[final] ).
cnf(c_0_898,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_703,
[final] ).
cnf(c_0_899,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_704,
[final] ).
cnf(c_0_900,plain,
( c_Type_Otyping(X1,X4,X3)
| ~ c_Type_Otyping(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
c_0_705,
[final] ).
cnf(c_0_901,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_706,
[final] ).
cnf(c_0_902,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_707,
[final] ).
cnf(c_0_903,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_708,
[final] ).
cnf(c_0_904,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_709,
[final] ).
cnf(c_0_905,plain,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_710,
[final] ).
cnf(c_0_906,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_711,
[final] ).
cnf(c_0_907,plain,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
c_0_712,
[final] ).
cnf(c_0_908,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_713,
[final] ).
cnf(c_0_909,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_714,
[final] ).
cnf(c_0_910,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_715,
[final] ).
cnf(c_0_911,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_716,
[final] ).
cnf(c_0_912,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_717,
[final] ).
cnf(c_0_913,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_718,
[final] ).
cnf(c_0_914,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_719,
[final] ).
cnf(c_0_915,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_720,
[final] ).
cnf(c_0_916,plain,
( X1 = X2
| c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
c_0_721,
[final] ).
cnf(c_0_917,plain,
( X1 = X2
| c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
c_0_722,
[final] ).
cnf(c_0_918,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_723,
[final] ).
cnf(c_0_919,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_724,
[final] ).
cnf(c_0_920,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_725,
[final] ).
cnf(c_0_921,plain,
( X1 = X2
| c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
c_0_726,
[final] ).
cnf(c_0_922,plain,
( X1 = X2
| c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
c_0_727,
[final] ).
cnf(c_0_923,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
c_0_728,
[final] ).
cnf(c_0_924,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_729,
[final] ).
cnf(c_0_925,plain,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
c_0_730,
[final] ).
cnf(c_0_926,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X1,X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_731,
[final] ).
cnf(c_0_927,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_732,
[final] ).
cnf(c_0_928,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_733,
[final] ).
cnf(c_0_929,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_734,
[final] ).
cnf(c_0_930,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_735,
[final] ).
cnf(c_0_931,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_736,
[final] ).
cnf(c_0_932,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_737,
[final] ).
cnf(c_0_933,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2) ),
c_0_738,
[final] ).
cnf(c_0_934,plain,
( X1 = X2
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4) ),
c_0_739,
[final] ).
cnf(c_0_935,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X3),X1) != hAPP(hAPP(c_Type_Otype_OFun,X4),X2) ),
c_0_740,
[final] ).
cnf(c_0_936,plain,
( X1 = X2
| hAPP(hAPP(c_Type_Otype_OFun,X1),X3) != hAPP(hAPP(c_Type_Otype_OFun,X2),X4) ),
c_0_741,
[final] ).
cnf(c_0_937,plain,
( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
c_0_742,
[final] ).
cnf(c_0_938,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_743,
[final] ).
cnf(c_0_939,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_744,
[final] ).
cnf(c_0_940,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_745,
[final] ).
cnf(c_0_941,plain,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
c_0_746,
[final] ).
cnf(c_0_942,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_747,
[final] ).
cnf(c_0_943,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
c_0_748,
[final] ).
cnf(c_0_944,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_749,
[final] ).
cnf(c_0_945,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_750,
[final] ).
cnf(c_0_946,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_751,
[final] ).
cnf(c_0_947,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
c_0_752,
[final] ).
cnf(c_0_948,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
c_0_753,
[final] ).
cnf(c_0_949,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != c_List_Olist_ONil(X2) ),
c_0_754,
[final] ).
cnf(c_0_950,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != c_List_Olist_ONil(X2) ),
c_0_755,
[final] ).
cnf(c_0_951,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_756,
[final] ).
cnf(c_0_952,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_757,
[final] ).
cnf(c_0_953,plain,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_758,
[final] ).
cnf(c_0_954,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
c_0_759,
[final] ).
cnf(c_0_955,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
c_0_760,
[final] ).
cnf(c_0_956,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
c_0_761,
[final] ).
cnf(c_0_957,plain,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
c_0_762,
[final] ).
cnf(c_0_958,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
c_0_763,
[final] ).
cnf(c_0_959,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_764,
[final] ).
cnf(c_0_960,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_765,
[final] ).
cnf(c_0_961,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_766,
[final] ).
cnf(c_0_962,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_767,
[final] ).
cnf(c_0_963,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_768,
[final] ).
cnf(c_0_964,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_769,
[final] ).
cnf(c_0_965,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_770,
[final] ).
cnf(c_0_966,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_771,
[final] ).
cnf(c_0_967,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_772,
[final] ).
cnf(c_0_968,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_773,
[final] ).
cnf(c_0_969,plain,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| ~ class_Nat_Osemiring__char__0(X3) ),
c_0_774,
[final] ).
cnf(c_0_970,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_775,
[final] ).
cnf(c_0_971,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_776,
[final] ).
cnf(c_0_972,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
c_0_777,
[final] ).
cnf(c_0_973,plain,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
c_0_778,
[final] ).
cnf(c_0_974,plain,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
c_0_779,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_780_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_780]) ).
cnf(c_0_780_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_780]) ).
cnf(c_0_780_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_780]) ).
cnf(c_0_780_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_780]) ).
cnf(c_0_781_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_781]) ).
cnf(c_0_781_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_781]) ).
cnf(c_0_782_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_782]) ).
cnf(c_0_782_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_782]) ).
cnf(c_0_782_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_782]) ).
cnf(c_0_782_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_782]) ).
cnf(c_0_783_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_783]) ).
cnf(c_0_783_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_783]) ).
cnf(c_0_784_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_784]) ).
cnf(c_0_784_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_784]) ).
cnf(c_0_785_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_785]) ).
cnf(c_0_785_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_785]) ).
cnf(c_0_786_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_786]) ).
cnf(c_0_786_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_786]) ).
cnf(c_0_787_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_787]) ).
cnf(c_0_787_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_787]) ).
cnf(c_0_787_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_787]) ).
cnf(c_0_788_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_788]) ).
cnf(c_0_788_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_788]) ).
cnf(c_0_788_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_788]) ).
cnf(c_0_789_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_789]) ).
cnf(c_0_789_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_789]) ).
cnf(c_0_789_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_789]) ).
cnf(c_0_790_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_790]) ).
cnf(c_0_790_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_790]) ).
cnf(c_0_791_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_791]) ).
cnf(c_0_791_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_791]) ).
cnf(c_0_792_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_792]) ).
cnf(c_0_792_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_792]) ).
cnf(c_0_793_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_793]) ).
cnf(c_0_793_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_793]) ).
cnf(c_0_794_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_794]) ).
cnf(c_0_794_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_794]) ).
cnf(c_0_794_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_794]) ).
cnf(c_0_795_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_795]) ).
cnf(c_0_795_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_795]) ).
cnf(c_0_796_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_796]) ).
cnf(c_0_796_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_796]) ).
cnf(c_0_797_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_797]) ).
cnf(c_0_797_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_797]) ).
cnf(c_0_798_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_798]) ).
cnf(c_0_798_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_798]) ).
cnf(c_0_799_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_799]) ).
cnf(c_0_799_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_799]) ).
cnf(c_0_800_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_800]) ).
cnf(c_0_800_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_800]) ).
cnf(c_0_801_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_801]) ).
cnf(c_0_801_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_801]) ).
cnf(c_0_802_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_802]) ).
cnf(c_0_802_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_802]) ).
cnf(c_0_803_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_803]) ).
cnf(c_0_803_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_803]) ).
cnf(c_0_804_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_804]) ).
cnf(c_0_804_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_804]) ).
cnf(c_0_805_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_805]) ).
cnf(c_0_805_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_805]) ).
cnf(c_0_806_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_806]) ).
cnf(c_0_806_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_806]) ).
cnf(c_0_807_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_807]) ).
cnf(c_0_807_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_807]) ).
cnf(c_0_808_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_808]) ).
cnf(c_0_808_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_808]) ).
cnf(c_0_809_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_809]) ).
cnf(c_0_809_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_809]) ).
cnf(c_0_810_0,axiom,
( c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_810]) ).
cnf(c_0_810_1,axiom,
( ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)
| c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_810]) ).
cnf(c_0_811_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_811]) ).
cnf(c_0_811_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_811]) ).
cnf(c_0_812_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_812]) ).
cnf(c_0_812_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_812]) ).
cnf(c_0_813_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_813]) ).
cnf(c_0_813_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_813]) ).
cnf(c_0_814_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_814]) ).
cnf(c_0_814_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_814]) ).
cnf(c_0_815_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_815]) ).
cnf(c_0_815_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_815]) ).
cnf(c_0_816_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_816]) ).
cnf(c_0_816_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_816]) ).
cnf(c_0_817_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_817]) ).
cnf(c_0_817_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_817]) ).
cnf(c_0_818_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_818]) ).
cnf(c_0_818_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_818]) ).
cnf(c_0_819_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_819]) ).
cnf(c_0_819_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_819]) ).
cnf(c_0_819_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_819]) ).
cnf(c_0_820_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_820]) ).
cnf(c_0_820_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_820]) ).
cnf(c_0_820_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_820]) ).
cnf(c_0_821_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_821]) ).
cnf(c_0_821_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_821]) ).
cnf(c_0_821_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_821]) ).
cnf(c_0_822_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_822]) ).
cnf(c_0_822_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_822]) ).
cnf(c_0_822_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_822]) ).
cnf(c_0_823_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_823]) ).
cnf(c_0_823_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_823]) ).
cnf(c_0_824_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_824]) ).
cnf(c_0_824_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_824]) ).
cnf(c_0_824_2,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_824]) ).
cnf(c_0_824_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_824]) ).
cnf(c_0_824_4,axiom,
( ~ c_Type_Otyping(X2,X6,X4)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_824]) ).
cnf(c_0_824_5,axiom,
( hAPP(hAPP(c_Type_Otype_OFun,X4),X7) != v_T____
| ~ c_Type_Otyping(X2,X6,X4)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_824]) ).
cnf(c_0_825_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_825]) ).
cnf(c_0_825_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_825]) ).
cnf(c_0_825_2,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_825]) ).
cnf(c_0_825_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| ~ c_Type_Otyping(X2,X6,X4)
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_825]) ).
cnf(c_0_825_4,axiom,
( ~ c_Type_Otyping(X2,X6,X4)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3)))
| hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____ ),
inference(literals_permutation,[status(thm)],[c_0_825]) ).
cnf(c_0_825_5,axiom,
( hAPP(hAPP(c_Type_Otype_OFun,X7),X4) != v_T____
| ~ c_Type_Otyping(X2,X6,X4)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X6))
| ~ c_Type_Otyping(c_Type_Oshift(X2,X3,X4,tc_Type_Otype),X1,X5)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X1,X6,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_825]) ).
cnf(c_0_826_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_826]) ).
cnf(c_0_826_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_826]) ).
cnf(c_0_827_0,axiom,
( c_Type_Otyping(X1,c_Lambda_Osubst(X2,X3,X4),X5)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_827]) ).
cnf(c_0_827_1,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| c_Type_Otyping(X1,c_Lambda_Osubst(X2,X3,X4),X5)
| ~ c_Type_Otyping(X1,X3,X6) ),
inference(literals_permutation,[status(thm)],[c_0_827]) ).
cnf(c_0_827_2,axiom,
( ~ c_Type_Otyping(X1,X3,X6)
| ~ c_Type_Otyping(c_Type_Oshift(X1,X4,X6,tc_Type_Otype),X2,X5)
| c_Type_Otyping(X1,c_Lambda_Osubst(X2,X3,X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_827]) ).
cnf(c_0_828_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_828]) ).
cnf(c_0_828_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_828]) ).
cnf(c_0_828_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_828]) ).
cnf(c_0_829_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_829]) ).
cnf(c_0_829_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_829]) ).
cnf(c_0_830_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_830]) ).
cnf(c_0_830_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_830]) ).
cnf(c_0_831_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_831]) ).
cnf(c_0_831_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_831]) ).
cnf(c_0_831_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_831]) ).
cnf(c_0_832_0,axiom,
( c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),hAPP(hAPP(c_Type_Otype_OFun,X2),X4))
| ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_832]) ).
cnf(c_0_832_1,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X3,X4)
| c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),hAPP(hAPP(c_Type_Otype_OFun,X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_832]) ).
cnf(c_0_833_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_833]) ).
cnf(c_0_833_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_833]) ).
cnf(c_0_833_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_833]) ).
cnf(c_0_834_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_834]) ).
cnf(c_0_834_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_834]) ).
cnf(c_0_835_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_835]) ).
cnf(c_0_835_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_835]) ).
cnf(c_0_836_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_836]) ).
cnf(c_0_836_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_836]) ).
cnf(c_0_837_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_837]) ).
cnf(c_0_837_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_837]) ).
cnf(c_0_838_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_838]) ).
cnf(c_0_838_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_838]) ).
cnf(c_0_839_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_839]) ).
cnf(c_0_839_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_839]) ).
cnf(c_0_840_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_840]) ).
cnf(c_0_840_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_840]) ).
cnf(c_0_841_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_841]) ).
cnf(c_0_841_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_841]) ).
cnf(c_0_842_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_842]) ).
cnf(c_0_842_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_842]) ).
cnf(c_0_843_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_843]) ).
cnf(c_0_843_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_843]) ).
cnf(c_0_843_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_843]) ).
cnf(c_0_844_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_844]) ).
cnf(c_0_844_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_844]) ).
cnf(c_0_844_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_844]) ).
cnf(c_0_845_0,axiom,
( c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3))
| ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_845]) ).
cnf(c_0_845_1,axiom,
( ~ c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)
| c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_845]) ).
cnf(c_0_846_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_846]) ).
cnf(c_0_846_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_846]) ).
cnf(c_0_846_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_846]) ).
cnf(c_0_847_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_847]) ).
cnf(c_0_847_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_847]) ).
cnf(c_0_848_0,axiom,
( c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_Lambda_Olift(X2,X4),X3)
| ~ c_Type_Otyping(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_848]) ).
cnf(c_0_848_1,axiom,
( ~ c_Type_Otyping(X1,X2,X3)
| c_Type_Otyping(c_Type_Oshift(X1,X4,X5,tc_Type_Otype),c_Lambda_Olift(X2,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_848]) ).
cnf(c_0_849_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_849]) ).
cnf(c_0_849_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_849]) ).
cnf(c_0_850_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_850]) ).
cnf(c_0_850_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_850]) ).
cnf(c_0_851_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_851]) ).
cnf(c_0_851_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_851]) ).
cnf(c_0_852_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_852]) ).
cnf(c_0_852_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_852]) ).
cnf(c_0_853_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_853]) ).
cnf(c_0_853_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_853]) ).
cnf(c_0_853_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_853]) ).
cnf(c_0_854_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_854]) ).
cnf(c_0_854_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_854]) ).
cnf(c_0_854_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_854]) ).
cnf(c_0_855_0,axiom,
( hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_855]) ).
cnf(c_0_855_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| hAPP(c_Type_Oshift(X3,X2,X4,X5),X1) = hAPP(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_855]) ).
cnf(c_0_856_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_856]) ).
cnf(c_0_856_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_856]) ).
cnf(c_0_857_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_857]) ).
cnf(c_0_857_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_857]) ).
cnf(c_0_858_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_858]) ).
cnf(c_0_858_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_858]) ).
cnf(c_0_859_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_859]) ).
cnf(c_0_859_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_859]) ).
cnf(c_0_860_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_860]) ).
cnf(c_0_860_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_860]) ).
cnf(c_0_861_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_861]) ).
cnf(c_0_861_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_861]) ).
cnf(c_0_861_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_861]) ).
cnf(c_0_862_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_862]) ).
cnf(c_0_862_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_862]) ).
cnf(c_0_862_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_862]) ).
cnf(c_0_863_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_863]) ).
cnf(c_0_863_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_863]) ).
cnf(c_0_864_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_864]) ).
cnf(c_0_864_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_864]) ).
cnf(c_0_864_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_864]) ).
cnf(c_0_864_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_864]) ).
cnf(c_0_865_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_865]) ).
cnf(c_0_865_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_865]) ).
cnf(c_0_865_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_865]) ).
cnf(c_0_866_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_866]) ).
cnf(c_0_866_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_866]) ).
cnf(c_0_866_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_866]) ).
cnf(c_0_867_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_867]) ).
cnf(c_0_867_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_867]) ).
cnf(c_0_868_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_868]) ).
cnf(c_0_868_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_868]) ).
cnf(c_0_869_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_869]) ).
cnf(c_0_869_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_869]) ).
cnf(c_0_870_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_870]) ).
cnf(c_0_870_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_870]) ).
cnf(c_0_871_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_871]) ).
cnf(c_0_871_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_871]) ).
cnf(c_0_872_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_872]) ).
cnf(c_0_872_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_872]) ).
cnf(c_0_872_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_872]) ).
cnf(c_0_873_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_873]) ).
cnf(c_0_873_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_873]) ).
cnf(c_0_873_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_873]) ).
cnf(c_0_874_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_874]) ).
cnf(c_0_874_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_874]) ).
cnf(c_0_874_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_874]) ).
cnf(c_0_875_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_875]) ).
cnf(c_0_875_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_875]) ).
cnf(c_0_875_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_875]) ).
cnf(c_0_875_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_875]) ).
cnf(c_0_876_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_876]) ).
cnf(c_0_876_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_876]) ).
cnf(c_0_876_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_876]) ).
cnf(c_0_876_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_876]) ).
cnf(c_0_877_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_877]) ).
cnf(c_0_877_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_877]) ).
cnf(c_0_877_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_877]) ).
cnf(c_0_878_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_878]) ).
cnf(c_0_878_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_878]) ).
cnf(c_0_878_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_878]) ).
cnf(c_0_879_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_879]) ).
cnf(c_0_879_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_879]) ).
cnf(c_0_879_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_879]) ).
cnf(c_0_880_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_880]) ).
cnf(c_0_880_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_880]) ).
cnf(c_0_880_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_880]) ).
cnf(c_0_881_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_881]) ).
cnf(c_0_881_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_881]) ).
cnf(c_0_882_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_882]) ).
cnf(c_0_882_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_882]) ).
cnf(c_0_882_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_882]) ).
cnf(c_0_882_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_882]) ).
cnf(c_0_883_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_883]) ).
cnf(c_0_883_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_883]) ).
cnf(c_0_883_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_883]) ).
cnf(c_0_884_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_884]) ).
cnf(c_0_884_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_884]) ).
cnf(c_0_884_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_884]) ).
cnf(c_0_885_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_885]) ).
cnf(c_0_885_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_885]) ).
cnf(c_0_885_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_885]) ).
cnf(c_0_886_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_886]) ).
cnf(c_0_886_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_886]) ).
cnf(c_0_886_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_886]) ).
cnf(c_0_887_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_887]) ).
cnf(c_0_887_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_887]) ).
cnf(c_0_888_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_888]) ).
cnf(c_0_888_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_888]) ).
cnf(c_0_889_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_889]) ).
cnf(c_0_889_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_889]) ).
cnf(c_0_890_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_890]) ).
cnf(c_0_890_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_890]) ).
cnf(c_0_891_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_891]) ).
cnf(c_0_891_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_891]) ).
cnf(c_0_892_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_892]) ).
cnf(c_0_892_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_892]) ).
cnf(c_0_893_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_893]) ).
cnf(c_0_893_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_893]) ).
cnf(c_0_894_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_894]) ).
cnf(c_0_894_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_894]) ).
cnf(c_0_894_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_894]) ).
cnf(c_0_895_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_895]) ).
cnf(c_0_895_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_895]) ).
cnf(c_0_895_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_895]) ).
cnf(c_0_896_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_896]) ).
cnf(c_0_896_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_896]) ).
cnf(c_0_896_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_896]) ).
cnf(c_0_897_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_897]) ).
cnf(c_0_897_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_897]) ).
cnf(c_0_897_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_897]) ).
cnf(c_0_898_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_898]) ).
cnf(c_0_898_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_898]) ).
cnf(c_0_898_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_898]) ).
cnf(c_0_899_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_899]) ).
cnf(c_0_899_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_899]) ).
cnf(c_0_900_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_900]) ).
cnf(c_0_900_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_900]) ).
cnf(c_0_900_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_900]) ).
cnf(c_0_901_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_901]) ).
cnf(c_0_901_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2)))) ),
inference(literals_permutation,[status(thm)],[c_0_901]) ).
cnf(c_0_902_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_902]) ).
cnf(c_0_902_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_902]) ).
cnf(c_0_902_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_902]) ).
cnf(c_0_902_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_902]) ).
cnf(c_0_903_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_903]) ).
cnf(c_0_903_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_903]) ).
cnf(c_0_903_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_903]) ).
cnf(c_0_903_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_903]) ).
cnf(c_0_904_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_904]) ).
cnf(c_0_904_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_904]) ).
cnf(c_0_905_0,axiom,
( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_905]) ).
cnf(c_0_905_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_905]) ).
cnf(c_0_905_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
| c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_905]) ).
cnf(c_0_906_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_906]) ).
cnf(c_0_906_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_906]) ).
cnf(c_0_906_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_906]) ).
cnf(c_0_907_0,axiom,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_907]) ).
cnf(c_0_907_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
| ~ class_Ring__and__Field_Oordered__semidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_907]) ).
cnf(c_0_907_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_907]) ).
cnf(c_0_908_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_908]) ).
cnf(c_0_908_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_908]) ).
cnf(c_0_909_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_909]) ).
cnf(c_0_909_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_909]) ).
cnf(c_0_909_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_909]) ).
cnf(c_0_909_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_909]) ).
cnf(c_0_910_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_910]) ).
cnf(c_0_910_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_910]) ).
cnf(c_0_910_2,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_910]) ).
cnf(c_0_911_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_911]) ).
cnf(c_0_911_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_911]) ).
cnf(c_0_911_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_911]) ).
cnf(c_0_911_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_911]) ).
cnf(c_0_912_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_912]) ).
cnf(c_0_912_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_912]) ).
cnf(c_0_912_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_912]) ).
cnf(c_0_913_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_913]) ).
cnf(c_0_913_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_913]) ).
cnf(c_0_913_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_913]) ).
cnf(c_0_914_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_914]) ).
cnf(c_0_914_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_914]) ).
cnf(c_0_914_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_914]) ).
cnf(c_0_915_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_915]) ).
cnf(c_0_915_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_915]) ).
cnf(c_0_915_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_915]) ).
cnf(c_0_916_0,axiom,
( X1 = X2
| c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_916]) ).
cnf(c_0_916_1,axiom,
( c_List_Oappend(X3,X1,X4) != c_List_Oappend(X3,X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_916]) ).
cnf(c_0_917_0,axiom,
( X1 = X2
| c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_917]) ).
cnf(c_0_917_1,axiom,
( c_List_Oappend(X1,X3,X4) != c_List_Oappend(X2,X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_917]) ).
cnf(c_0_918_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_918]) ).
cnf(c_0_918_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_918]) ).
cnf(c_0_918_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_918]) ).
cnf(c_0_919_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_919]) ).
cnf(c_0_919_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_919]) ).
cnf(c_0_919_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_919]) ).
cnf(c_0_920_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_920]) ).
cnf(c_0_920_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_920]) ).
cnf(c_0_920_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_920]) ).
cnf(c_0_921_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_921]) ).
cnf(c_0_921_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_921]) ).
cnf(c_0_922_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_922]) ).
cnf(c_0_922_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_922]) ).
cnf(c_0_923_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_923]) ).
cnf(c_0_923_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_923]) ).
cnf(c_0_924_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_924]) ).
cnf(c_0_924_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_924]) ).
cnf(c_0_925_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_925]) ).
cnf(c_0_925_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_925]) ).
cnf(c_0_926_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_926]) ).
cnf(c_0_926_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_926]) ).
cnf(c_0_927_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_927]) ).
cnf(c_0_927_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_927]) ).
cnf(c_0_927_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_927]) ).
cnf(c_0_928_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_928]) ).
cnf(c_0_928_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_928]) ).
cnf(c_0_928_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_928]) ).
cnf(c_0_928_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_928]) ).
cnf(c_0_929_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_929]) ).
cnf(c_0_929_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_929]) ).
cnf(c_0_929_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_929]) ).
cnf(c_0_929_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_929]) ).
cnf(c_0_930_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_930]) ).
cnf(c_0_930_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_930]) ).
cnf(c_0_930_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_930]) ).
cnf(c_0_930_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_930]) ).
cnf(c_0_931_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_931]) ).
cnf(c_0_931_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_931]) ).
cnf(c_0_931_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_931]) ).
cnf(c_0_931_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_931]) ).
cnf(c_0_932_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_932]) ).
cnf(c_0_932_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_932]) ).
cnf(c_0_932_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_932]) ).
cnf(c_0_932_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_932]) ).
cnf(c_0_933_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_933]) ).
cnf(c_0_933_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_933]) ).
cnf(c_0_934_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_934]) ).
cnf(c_0_934_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_934]) ).
cnf(c_0_935_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_935]) ).
cnf(c_0_935_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_935]) ).
cnf(c_0_936_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_936]) ).
cnf(c_0_936_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_936]) ).
cnf(c_0_937_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_937]) ).
cnf(c_0_937_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_937]) ).
cnf(c_0_938_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_938]) ).
cnf(c_0_938_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_938]) ).
cnf(c_0_939_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_939]) ).
cnf(c_0_939_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_939]) ).
cnf(c_0_940_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_940]) ).
cnf(c_0_940_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_940]) ).
cnf(c_0_941_0,axiom,
( hAPP(X1,X2) = X3
| ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_941]) ).
cnf(c_0_941_1,axiom,
( ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3)
| hAPP(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_941]) ).
cnf(c_0_942_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_942]) ).
cnf(c_0_942_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_942]) ).
cnf(c_0_942_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_942]) ).
cnf(c_0_943_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_943]) ).
cnf(c_0_943_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_943]) ).
cnf(c_0_943_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_943]) ).
cnf(c_0_944_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_944]) ).
cnf(c_0_944_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_944]) ).
cnf(c_0_945_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_945]) ).
cnf(c_0_945_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_945]) ).
cnf(c_0_945_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_945]) ).
cnf(c_0_945_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_945]) ).
cnf(c_0_946_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_946]) ).
cnf(c_0_946_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_946]) ).
cnf(c_0_946_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_946]) ).
cnf(c_0_947_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_947]) ).
cnf(c_0_947_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_947]) ).
cnf(c_0_948_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_948]) ).
cnf(c_0_948_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_948]) ).
cnf(c_0_949_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_949]) ).
cnf(c_0_949_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_949]) ).
cnf(c_0_950_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_950]) ).
cnf(c_0_950_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_950]) ).
cnf(c_0_951_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_951]) ).
cnf(c_0_951_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_951]) ).
cnf(c_0_952_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_952]) ).
cnf(c_0_952_1,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_952]) ).
cnf(c_0_953_0,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_953]) ).
cnf(c_0_953_1,axiom,
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_953]) ).
cnf(c_0_954_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_954]) ).
cnf(c_0_954_1,axiom,
( c_List_Oappend(X1,X3,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_954]) ).
cnf(c_0_955_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X1,X3,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_955]) ).
cnf(c_0_955_1,axiom,
( c_List_Oappend(X1,X3,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_955]) ).
cnf(c_0_956_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_956]) ).
cnf(c_0_956_1,axiom,
( c_List_Oappend(X3,X1,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_956]) ).
cnf(c_0_957_0,axiom,
( X1 = c_List_Olist_ONil(X2)
| c_List_Oappend(X3,X1,X2) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_957]) ).
cnf(c_0_957_1,axiom,
( c_List_Oappend(X3,X1,X2) != X3
| X1 = c_List_Olist_ONil(X2) ),
inference(literals_permutation,[status(thm)],[c_0_957]) ).
cnf(c_0_958_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_958]) ).
cnf(c_0_958_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_958]) ).
cnf(c_0_959_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_959]) ).
cnf(c_0_959_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_959]) ).
cnf(c_0_960_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_960]) ).
cnf(c_0_960_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_960]) ).
cnf(c_0_960_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_960]) ).
cnf(c_0_961_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_961]) ).
cnf(c_0_961_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_961]) ).
cnf(c_0_962_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_962]) ).
cnf(c_0_962_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_962]) ).
cnf(c_0_963_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_963]) ).
cnf(c_0_963_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_963]) ).
cnf(c_0_964_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_964]) ).
cnf(c_0_964_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_964]) ).
cnf(c_0_965_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_965]) ).
cnf(c_0_965_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_965]) ).
cnf(c_0_966_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_966]) ).
cnf(c_0_966_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_966]) ).
cnf(c_0_967_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_967]) ).
cnf(c_0_967_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_967]) ).
cnf(c_0_968_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_968]) ).
cnf(c_0_968_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_968]) ).
cnf(c_0_969_0,axiom,
( X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| ~ class_Nat_Osemiring__char__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_969]) ).
cnf(c_0_969_1,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| X1 = X2
| ~ class_Nat_Osemiring__char__0(X3) ),
inference(literals_permutation,[status(thm)],[c_0_969]) ).
cnf(c_0_969_2,axiom,
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_969]) ).
cnf(c_0_970_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_970]) ).
cnf(c_0_970_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_970]) ).
cnf(c_0_971_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_971]) ).
cnf(c_0_971_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_971]) ).
cnf(c_0_972_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_972]) ).
cnf(c_0_972_1,axiom,
( ~ class_Ring__and__Field_Osemiring__1(X1)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_972]) ).
cnf(c_0_973_0,axiom,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
inference(literals_permutation,[status(thm)],[c_0_973]) ).
cnf(c_0_973_1,axiom,
( c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_973]) ).
cnf(c_0_974_0,axiom,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
inference(literals_permutation,[status(thm)],[c_0_974]) ).
cnf(c_0_974_1,axiom,
( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_974]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_491,negated_conjecture,
~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_1_492,negated_conjecture,
~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_2_493,negated_conjecture,
~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
c_0_1 ).
cnf(c_0_3_494,negated_conjecture,
~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_495,negated_conjecture,
~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_114,plain,
( ~ c_Type_Otyping(X0,X1,X2)
| ~ c_Type_Otyping(c_Type_Oshift(X0,X3,X2,tc_Type_Otype),X4,X5)
| c_Type_Otyping(X0,c_Lambda_Osubst(X4,X1,X3),X5) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_8f66cc.p',c_0_827_0) ).
cnf(c_892,plain,
( ~ c_Type_Otyping(X0,X1,X2)
| ~ c_Type_Otyping(c_Type_Oshift(X0,X3,X2,tc_Type_Otype),X4,X5)
| c_Type_Otyping(X0,c_Lambda_Osubst(X4,X1,X3),X5) ),
inference(copy,[status(esa)],[c_114]) ).
cnf(c_23233,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,X0,v_T____,tc_Type_Otype),X1,X2)
| c_Type_Otyping(v_e____,c_Lambda_Osubst(X1,v_u____,X0),X2)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____) ),
inference(instantiation,[status(thm)],[c_892]) ).
cnf(c_24679,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____)
| c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____)
| ~ c_Type_Otyping(v_e____,v_u____,v_T____) ),
inference(instantiation,[status(thm)],[c_23233]) ).
cnf(c_500,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox/tmp/iprover_modulo_8f66cc.p',c_0_474_0) ).
cnf(c_501,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
file('/export/starexec/sandbox/tmp/iprover_modulo_8f66cc.p',c_0_473_0) ).
cnf(c_583,negated_conjecture,
~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
file('/export/starexec/sandbox/tmp/iprover_modulo_8f66cc.p',c_0_4) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_24679,c_500,c_501,c_583]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : LCL817-1 : TPTP v8.1.0. Released v4.1.0.
% 0.09/0.13 % Command : iprover_modulo %s %d
% 0.14/0.33 % Computer : n025.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Mon Jul 4 17:04:26 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % Running in mono-core mode
% 0.20/0.43 % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.43 % Orientation found
% 0.20/0.43 % 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_57ae22.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_8f66cc.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_992381 | grep -v "SZS"
% 0.20/0.45
% 0.20/0.45 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.45
% 0.20/0.45 %
% 0.20/0.45 % ------ iProver source info
% 0.20/0.45
% 0.20/0.45 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.45 % git: non_committed_changes: true
% 0.20/0.45 % git: last_make_outside_of_git: true
% 0.20/0.45
% 0.20/0.45 %
% 0.20/0.45 % ------ Input Options
% 0.20/0.45
% 0.20/0.45 % --out_options all
% 0.20/0.45 % --tptp_safe_out true
% 0.20/0.45 % --problem_path ""
% 0.20/0.45 % --include_path ""
% 0.20/0.45 % --clausifier .//eprover
% 0.20/0.45 % --clausifier_options --tstp-format
% 0.20/0.45 % --stdin false
% 0.20/0.45 % --dbg_backtrace false
% 0.20/0.45 % --dbg_dump_prop_clauses false
% 0.20/0.45 % --dbg_dump_prop_clauses_file -
% 0.20/0.45 % --dbg_out_stat false
% 0.20/0.45
% 0.20/0.45 % ------ General Options
% 0.20/0.45
% 0.20/0.45 % --fof false
% 0.20/0.45 % --time_out_real 150.
% 0.20/0.45 % --time_out_prep_mult 0.2
% 0.20/0.45 % --time_out_virtual -1.
% 0.20/0.45 % --schedule none
% 0.20/0.45 % --ground_splitting input
% 0.20/0.45 % --splitting_nvd 16
% 0.20/0.45 % --non_eq_to_eq false
% 0.20/0.45 % --prep_gs_sim true
% 0.20/0.45 % --prep_unflatten false
% 0.20/0.45 % --prep_res_sim true
% 0.20/0.45 % --prep_upred true
% 0.20/0.45 % --res_sim_input true
% 0.20/0.45 % --clause_weak_htbl true
% 0.20/0.45 % --gc_record_bc_elim false
% 0.20/0.45 % --symbol_type_check false
% 0.20/0.45 % --clausify_out false
% 0.20/0.45 % --large_theory_mode false
% 0.20/0.45 % --prep_sem_filter none
% 0.20/0.45 % --prep_sem_filter_out false
% 0.20/0.45 % --preprocessed_out false
% 0.20/0.45 % --sub_typing false
% 0.20/0.45 % --brand_transform false
% 0.20/0.45 % --pure_diseq_elim true
% 0.20/0.45 % --min_unsat_core false
% 0.20/0.45 % --pred_elim true
% 0.20/0.45 % --add_important_lit false
% 0.20/0.45 % --soft_assumptions false
% 0.20/0.45 % --reset_solvers false
% 0.20/0.45 % --bc_imp_inh []
% 0.20/0.45 % --conj_cone_tolerance 1.5
% 0.20/0.45 % --prolific_symb_bound 500
% 0.20/0.45 % --lt_threshold 2000
% 0.20/0.45
% 0.20/0.45 % ------ SAT Options
% 0.20/0.45
% 0.20/0.45 % --sat_mode false
% 0.20/0.45 % --sat_fm_restart_options ""
% 0.20/0.45 % --sat_gr_def false
% 0.20/0.45 % --sat_epr_types true
% 0.20/0.45 % --sat_non_cyclic_types false
% 0.20/0.45 % --sat_finite_models false
% 0.20/0.45 % --sat_fm_lemmas false
% 0.20/0.45 % --sat_fm_prep false
% 0.20/0.45 % --sat_fm_uc_incr true
% 0.20/0.45 % --sat_out_model small
% 0.20/0.45 % --sat_out_clauses false
% 0.20/0.45
% 0.20/0.45 % ------ QBF Options
% 0.20/0.45
% 0.20/0.45 % --qbf_mode false
% 0.20/0.45 % --qbf_elim_univ true
% 0.20/0.45 % --qbf_sk_in true
% 0.20/0.45 % --qbf_pred_elim true
% 0.20/0.45 % --qbf_split 32
% 0.20/0.45
% 0.20/0.45 % ------ BMC1 Options
% 0.20/0.45
% 0.20/0.45 % --bmc1_incremental false
% 0.20/0.45 % --bmc1_axioms reachable_all
% 0.20/0.45 % --bmc1_min_bound 0
% 0.20/0.45 % --bmc1_max_bound -1
% 0.20/0.45 % --bmc1_max_bound_default -1
% 0.20/0.45 % --bmc1_symbol_reachability true
% 0.20/0.45 % --bmc1_property_lemmas false
% 0.20/0.45 % --bmc1_k_induction false
% 0.20/0.45 % --bmc1_non_equiv_states false
% 0.20/0.45 % --bmc1_deadlock false
% 0.20/0.45 % --bmc1_ucm false
% 0.20/0.45 % --bmc1_add_unsat_core none
% 0.20/0.45 % --bmc1_unsat_core_children false
% 0.20/0.45 % --bmc1_unsat_core_extrapolate_axioms false
% 0.20/0.45 % --bmc1_out_stat full
% 0.20/0.45 % --bmc1_ground_init false
% 0.20/0.45 % --bmc1_pre_inst_next_state false
% 0.20/0.45 % --bmc1_pre_inst_state false
% 0.20/0.45 % --bmc1_pre_inst_reach_state false
% 0.20/0.45 % --bmc1_out_unsat_core false
% 0.20/0.45 % --bmc1_aig_witness_out false
% 0.20/0.45 % --bmc1_verbose false
% 0.20/0.45 % --bmc1_dump_clauses_tptp false
% 2.03/2.31 % --bmc1_dump_unsat_core_tptp false
% 2.03/2.31 % --bmc1_dump_file -
% 2.03/2.31 % --bmc1_ucm_expand_uc_limit 128
% 2.03/2.31 % --bmc1_ucm_n_expand_iterations 6
% 2.03/2.31 % --bmc1_ucm_extend_mode 1
% 2.03/2.31 % --bmc1_ucm_init_mode 2
% 2.03/2.31 % --bmc1_ucm_cone_mode none
% 2.03/2.31 % --bmc1_ucm_reduced_relation_type 0
% 2.03/2.31 % --bmc1_ucm_relax_model 4
% 2.03/2.31 % --bmc1_ucm_full_tr_after_sat true
% 2.03/2.31 % --bmc1_ucm_expand_neg_assumptions false
% 2.03/2.31 % --bmc1_ucm_layered_model none
% 2.03/2.31 % --bmc1_ucm_max_lemma_size 10
% 2.03/2.31
% 2.03/2.31 % ------ AIG Options
% 2.03/2.31
% 2.03/2.31 % --aig_mode false
% 2.03/2.31
% 2.03/2.31 % ------ Instantiation Options
% 2.03/2.31
% 2.03/2.31 % --instantiation_flag true
% 2.03/2.31 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 2.03/2.31 % --inst_solver_per_active 750
% 2.03/2.31 % --inst_solver_calls_frac 0.5
% 2.03/2.31 % --inst_passive_queue_type priority_queues
% 2.03/2.31 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 2.03/2.31 % --inst_passive_queues_freq [25;2]
% 2.03/2.31 % --inst_dismatching true
% 2.03/2.31 % --inst_eager_unprocessed_to_passive true
% 2.03/2.31 % --inst_prop_sim_given true
% 2.03/2.31 % --inst_prop_sim_new false
% 2.03/2.31 % --inst_orphan_elimination true
% 2.03/2.31 % --inst_learning_loop_flag true
% 2.03/2.31 % --inst_learning_start 3000
% 2.03/2.31 % --inst_learning_factor 2
% 2.03/2.31 % --inst_start_prop_sim_after_learn 3
% 2.03/2.31 % --inst_sel_renew solver
% 2.03/2.31 % --inst_lit_activity_flag true
% 2.03/2.31 % --inst_out_proof true
% 2.03/2.31
% 2.03/2.31 % ------ Resolution Options
% 2.03/2.31
% 2.03/2.31 % --resolution_flag true
% 2.03/2.31 % --res_lit_sel kbo_max
% 2.03/2.31 % --res_to_prop_solver none
% 2.03/2.31 % --res_prop_simpl_new false
% 2.03/2.31 % --res_prop_simpl_given false
% 2.03/2.31 % --res_passive_queue_type priority_queues
% 2.03/2.31 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 2.03/2.31 % --res_passive_queues_freq [15;5]
% 2.03/2.31 % --res_forward_subs full
% 2.03/2.31 % --res_backward_subs full
% 2.03/2.31 % --res_forward_subs_resolution true
% 2.03/2.31 % --res_backward_subs_resolution true
% 2.03/2.31 % --res_orphan_elimination false
% 2.03/2.31 % --res_time_limit 1000.
% 2.03/2.31 % --res_out_proof true
% 2.03/2.31 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_57ae22.s
% 2.03/2.31 % --modulo true
% 2.03/2.31
% 2.03/2.31 % ------ Combination Options
% 2.03/2.31
% 2.03/2.31 % --comb_res_mult 1000
% 2.03/2.31 % --comb_inst_mult 300
% 2.03/2.31 % ------
% 2.03/2.31
% 2.03/2.31 % ------ Parsing...% successful
% 2.03/2.31
% 2.03/2.31 % ------ 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 %
% 2.03/2.31
% 2.03/2.31 % ------ Proving...
% 2.03/2.31 % ------ Problem Properties
% 2.03/2.31
% 2.03/2.31 %
% 2.03/2.31 % EPR false
% 2.03/2.31 % Horn false
% 2.03/2.31 % Has equality true
% 2.03/2.31
% 2.03/2.31 % % ------ Input Options Time Limit: Unbounded
% 2.03/2.31
% 2.03/2.31
% 2.03/2.31 Compiling...
% 2.03/2.31 Loading plugin: done.
% 2.03/2.31 Compiling...
% 2.03/2.31 Loading plugin: done.
% 2.03/2.31 Compiling...
% 2.03/2.31 Loading plugin: done.
% 2.03/2.31 Compiling...
% 2.03/2.31 Loading plugin: done.
% 2.03/2.31 Compiling...
% 2.03/2.31 Loading plugin: done.
% 2.03/2.31 Compiling...
% 2.03/2.31 Loading plugin: done.
% 2.03/2.31 Compiling...
% 2.03/2.31 Loading plugin: done.
% 2.03/2.31 Compiling...
% 2.03/2.31 Loading plugin: done.
% 2.03/2.31 Compiling...
% 2.03/2.31 Loading plugin: done.
% 2.03/2.31 Compiling...
% 2.03/2.31 Loading plugin: done.
% 2.03/2.31 Compiling...
% 2.03/2.31 Loading plugin: done.
% 2.03/2.31 Compiling...
% 2.03/2.31 Loading plugin: done.
% 2.03/2.31 Compiling...
% 2.03/2.31 Loading plugin: done.
% 2.03/2.31 Compiling...
% 2.03/2.31 Loading plugin: done.
% 2.03/2.31 % % ------ Current options:
% 2.03/2.31
% 2.03/2.31 % ------ Input Options
% 2.03/2.31
% 2.03/2.31 % --out_options all
% 2.03/2.31 % --tptp_safe_out true
% 2.03/2.31 % --problem_path ""
% 2.03/2.31 % --include_path ""
% 2.03/2.31 % --clausifier .//eprover
% 2.03/2.31 % --clausifier_options --tstp-format
% 2.03/2.31 % --stdin false
% 2.03/2.31 % --dbg_backtrace false
% 2.03/2.31 % --dbg_dump_prop_clauses false
% 2.03/2.31 % --dbg_dump_prop_clauses_file -
% 2.03/2.31 % --dbg_out_stat false
% 2.03/2.31
% 2.03/2.31 % ------ General Options
% 2.03/2.31
% 2.03/2.31 % --fof false
% 2.03/2.31 % --time_out_real 150.
% 2.03/2.31 % --time_out_prep_mult 0.2
% 2.03/2.31 % --time_out_virtual -1.
% 2.03/2.31 % --schedule none
% 2.03/2.31 % --ground_splitting input
% 2.03/2.31 % --splitting_nvd 16
% 2.03/2.31 % --non_eq_to_eq false
% 2.03/2.31 % --prep_gs_sim true
% 2.03/2.31 % --prep_unflatten false
% 2.03/2.31 % --prep_res_sim true
% 2.03/2.31 % --prep_upred true
% 2.03/2.31 % --res_sim_input true
% 2.03/2.31 % --clause_weak_htbl true
% 2.03/2.31 % --gc_record_bc_elim false
% 2.03/2.31 % --symbol_type_check false
% 2.03/2.31 % --clausify_out false
% 2.03/2.31 % --large_theory_mode false
% 2.03/2.31 % --prep_sem_filter none
% 2.03/2.31 % --prep_sem_filter_out false
% 2.03/2.31 % --preprocessed_out false
% 2.03/2.31 % --sub_typing false
% 2.03/2.31 % --brand_transform false
% 2.03/2.31 % --pure_diseq_elim true
% 2.03/2.31 % --min_unsat_core false
% 2.03/2.31 % --pred_elim true
% 2.03/2.31 % --add_important_lit false
% 2.03/2.31 % --soft_assumptions false
% 2.03/2.31 % --reset_solvers false
% 2.03/2.31 % --bc_imp_inh []
% 2.03/2.31 % --conj_cone_tolerance 1.5
% 2.03/2.31 % --prolific_symb_bound 500
% 2.03/2.31 % --lt_threshold 2000
% 2.03/2.31
% 2.03/2.31 % ------ SAT Options
% 2.03/2.31
% 2.03/2.31 % --sat_mode false
% 2.03/2.31 % --sat_fm_restart_options ""
% 2.03/2.31 % --sat_gr_def false
% 2.03/2.31 % --sat_epr_types true
% 2.03/2.31 % --sat_non_cyclic_types false
% 2.03/2.31 % --sat_finite_models false
% 2.03/2.31 % --sat_fm_lemmas false
% 2.03/2.31 % --sat_fm_prep false
% 2.03/2.31 % --sat_fm_uc_incr true
% 2.03/2.31 % --sat_out_model small
% 2.03/2.31 % --sat_out_clauses false
% 2.03/2.31
% 2.03/2.31 % ------ QBF Options
% 2.03/2.31
% 2.03/2.31 % --qbf_mode false
% 2.03/2.31 % --qbf_elim_univ true
% 2.03/2.31 % --qbf_sk_in true
% 2.03/2.31 % --qbf_pred_elim true
% 2.03/2.31 % --qbf_split 32
% 2.03/2.31
% 2.03/2.31 % ------ BMC1 Options
% 2.03/2.31
% 2.03/2.31 % --bmc1_incremental false
% 2.03/2.31 % --bmc1_axioms reachable_all
% 2.03/2.31 % --bmc1_min_bound 0
% 2.03/2.31 % --bmc1_max_bound -1
% 2.03/2.31 % --bmc1_max_bound_default -1
% 2.03/2.31 % --bmc1_symbol_reachability true
% 2.03/2.31 % --bmc1_property_lemmas false
% 2.03/2.31 % --bmc1_k_induction false
% 2.03/2.31 % --bmc1_non_equiv_states false
% 2.03/2.31 % --bmc1_deadlock false
% 2.03/2.31 % --bmc1_ucm false
% 2.03/2.31 % --bmc1_add_unsat_core none
% 2.03/2.31 % --bmc1_unsat_core_children false
% 2.03/2.31 % --bmc1_unsat_core_extrapolate_axioms false
% 2.03/2.31 % --bmc1_out_stat full
% 2.03/2.31 % --bmc1_ground_init false
% 2.03/2.31 % --bmc1_pre_inst_next_state false
% 2.03/2.31 % --bmc1_pre_inst_state false
% 2.03/2.31 % --bmc1_pre_inst_reach_state false
% 2.03/2.31 % --bmc1_out_unsat_core false
% 2.03/2.31 % --bmc1_aig_witness_out false
% 2.03/2.31 % --bmc1_verbose false
% 2.03/2.31 % --bmc1_dump_clauses_tptp false
% 2.03/2.31 % --bmc1_dump_unsat_core_tptp false
% 2.03/2.31 % --bmc1_dump_file -
% 2.03/2.31 % --bmc1_ucm_expand_uc_limit 128
% 2.03/2.31 % --bmc1_ucm_n_expand_iterations 6
% 2.03/2.31 % --bmc1_ucm_extend_mode 1
% 2.03/2.31 % --bmc1_ucm_init_mode 2
% 2.03/2.31 % --bmc1_ucm_cone_mode none
% 2.03/2.31 % --bmc1_ucm_reduced_relation_type 0
% 2.03/2.31 % --bmc1_ucm_relax_model 4
% 2.03/2.31 % --bmc1_ucm_full_tr_after_sat true
% 2.03/2.31 % --bmc1_ucm_expand_neg_assumptions false
% 2.03/2.31 % --bmc1_ucm_layered_model none
% 2.03/2.31 % --bmc1_ucm_max_lemma_size 10
% 2.03/2.31
% 2.03/2.31 % ------ AIG Options
% 2.03/2.31
% 2.03/2.31 % --aig_mode false
% 2.03/2.31
% 2.03/2.31 % ------ Instantiation Options
% 2.03/2.31
% 2.03/2.31 % --instantiation_flag true
% 3.37/3.65 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 3.37/3.65 % --inst_solver_per_active 750
% 3.37/3.65 % --inst_solver_calls_frac 0.5
% 3.37/3.65 % --inst_passive_queue_type priority_queues
% 3.37/3.65 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 3.37/3.65 % --inst_passive_queues_freq [25;2]
% 3.37/3.65 % --inst_dismatching true
% 3.37/3.65 % --inst_eager_unprocessed_to_passive true
% 3.37/3.65 % --inst_prop_sim_given true
% 3.37/3.65 % --inst_prop_sim_new false
% 3.37/3.65 % --inst_orphan_elimination true
% 3.37/3.65 % --inst_learning_loop_flag true
% 3.37/3.65 % --inst_learning_start 3000
% 3.37/3.65 % --inst_learning_factor 2
% 3.37/3.65 % --inst_start_prop_sim_after_learn 3
% 3.37/3.65 % --inst_sel_renew solver
% 3.37/3.65 % --inst_lit_activity_flag true
% 3.37/3.65 % --inst_out_proof true
% 3.37/3.65
% 3.37/3.65 % ------ Resolution Options
% 3.37/3.65
% 3.37/3.65 % --resolution_flag true
% 3.37/3.65 % --res_lit_sel kbo_max
% 3.37/3.65 % --res_to_prop_solver none
% 3.37/3.65 % --res_prop_simpl_new false
% 3.37/3.65 % --res_prop_simpl_given false
% 3.37/3.65 % --res_passive_queue_type priority_queues
% 3.37/3.65 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 3.37/3.65 % --res_passive_queues_freq [15;5]
% 3.37/3.65 % --res_forward_subs full
% 3.37/3.65 % --res_backward_subs full
% 3.37/3.65 % --res_forward_subs_resolution true
% 3.37/3.65 % --res_backward_subs_resolution true
% 3.37/3.65 % --res_orphan_elimination false
% 3.37/3.65 % --res_time_limit 1000.
% 3.37/3.65 % --res_out_proof true
% 3.37/3.65 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_57ae22.s
% 3.37/3.65 % --modulo true
% 3.37/3.65
% 3.37/3.65 % ------ Combination Options
% 3.37/3.65
% 3.37/3.65 % --comb_res_mult 1000
% 3.37/3.65 % --comb_inst_mult 300
% 3.37/3.65 % ------
% 3.37/3.65
% 3.37/3.65
% 3.37/3.65
% 3.37/3.65 % ------ Proving...
% 3.37/3.65 %
% 3.37/3.65
% 3.37/3.65
% 3.37/3.65 % ------ Statistics
% 3.37/3.65
% 3.37/3.65 % ------ General
% 3.37/3.65
% 3.37/3.65 % num_of_input_clauses: 584
% 3.37/3.65 % num_of_input_neg_conjectures: 1
% 3.37/3.65 % num_of_splits: 0
% 3.37/3.65 % num_of_split_atoms: 0
% 3.37/3.65 % num_of_sem_filtered_clauses: 0
% 3.37/3.65 % num_of_subtypes: 0
% 3.37/3.65 % monotx_restored_types: 0
% 3.37/3.65 % sat_num_of_epr_types: 0
% 3.37/3.65 % sat_num_of_non_cyclic_types: 0
% 3.37/3.65 % sat_guarded_non_collapsed_types: 0
% 3.37/3.65 % is_epr: 0
% 3.37/3.65 % is_horn: 0
% 3.37/3.65 % has_eq: 1
% 3.37/3.65 % num_pure_diseq_elim: 0
% 3.37/3.65 % simp_replaced_by: 0
% 3.37/3.65 % res_preprocessed: 2
% 3.37/3.65 % prep_upred: 0
% 3.37/3.65 % prep_unflattend: 0
% 3.37/3.65 % pred_elim_cands: 0
% 3.37/3.65 % pred_elim: 0
% 3.37/3.65 % pred_elim_cl: 0
% 3.37/3.65 % pred_elim_cycles: 0
% 3.37/3.65 % forced_gc_time: 0
% 3.37/3.65 % gc_basic_clause_elim: 0
% 3.37/3.65 % parsing_time: 0.02
% 3.37/3.65 % sem_filter_time: 0.
% 3.37/3.65 % pred_elim_time: 0.
% 3.37/3.65 % out_proof_time: 0.
% 3.37/3.65 % monotx_time: 0.
% 3.37/3.65 % subtype_inf_time: 0.
% 3.37/3.65 % unif_index_cands_time: 0.002
% 3.37/3.65 % unif_index_add_time: 0.002
% 3.37/3.65 % total_time: 3.207
% 3.37/3.65 % num_of_symbols: 101
% 3.37/3.65 % num_of_terms: 19067
% 3.37/3.65
% 3.37/3.65 % ------ Propositional Solver
% 3.37/3.65
% 3.37/3.65 % prop_solver_calls: 3
% 3.37/3.65 % prop_fast_solver_calls: 3
% 3.37/3.65 % prop_num_of_clauses: 1487
% 3.37/3.65 % prop_preprocess_simplified: 3354
% 3.37/3.65 % prop_fo_subsumed: 0
% 3.37/3.65 % prop_solver_time: 0.
% 3.37/3.65 % prop_fast_solver_time: 0.
% 3.37/3.65 % prop_unsat_core_time: 0.
% 3.37/3.65
% 3.37/3.65 % ------ QBF
% 3.37/3.65
% 3.37/3.65 % qbf_q_res: 0
% 3.37/3.65 % qbf_num_tautologies: 0
% 3.37/3.65 % qbf_prep_cycles: 0
% 3.37/3.65
% 3.37/3.65 % ------ BMC1
% 3.37/3.65
% 3.37/3.65 % bmc1_current_bound: -1
% 3.37/3.65 % bmc1_last_solved_bound: -1
% 3.37/3.65 % bmc1_unsat_core_size: -1
% 3.37/3.65 % bmc1_unsat_core_parents_size: -1
% 3.37/3.65 % bmc1_merge_next_fun: 0
% 3.37/3.65 % bmc1_unsat_core_clauses_time: 0.
% 3.37/3.65
% 3.37/3.65 % ------ Instantiation
% 3.37/3.65
% 3.37/3.65 % inst_num_of_clauses: 1012
% 3.37/3.65 % inst_num_in_passive: 513
% 3.37/3.65 % inst_num_in_active: 291
% 3.37/3.65 % inst_num_in_unprocessed: 206
% 3.37/3.65 % inst_num_of_loops: 293
% 3.37/3.65 % inst_num_of_learning_restarts: 0
% 3.37/3.65 % inst_num_moves_active_passive: 0
% 3.37/3.65 % inst_lit_activity: 97
% 3.37/3.65 % inst_lit_activity_moves: 0
% 3.37/3.65 % inst_num_tautologies: 0
% 3.37/3.65 % inst_num_prop_implied: 0
% 3.37/3.65 % inst_num_existing_simplified: 0
% 3.37/3.65 % inst_num_eq_res_simplified: 0
% 3.37/3.65 % inst_num_child_elim: 0
% 3.37/3.65 % inst_num_of_dismatching_blockings: 15
% 3.37/3.65 % inst_num_of_non_proper_insts: 491
% 3.37/3.65 % inst_num_of_duplicates: 671
% 3.37/3.65 % inst_inst_num_from_inst_to_res: 0
% 3.37/3.65 % inst_dismatching_checking_time: 0.
% 3.37/3.65
% 3.37/3.65 % ------ Resolution
% 3.37/3.65
% 3.37/3.65 % res_num_of_clauses: 6286
% 3.37/3.65 % res_num_in_passive: 5127
% 3.37/3.65 % res_num_in_active: 837
% 3.37/3.65 % res_num_of_loops: 1000
% 3.37/3.65 % res_forward_subset_subsumed: 581
% 3.37/3.65 % res_backward_subset_subsumed: 5
% 3.37/3.65 % res_forward_subsumed: 411
% 3.37/3.65 % res_backward_subsumed: 1
% 3.37/3.65 % res_forward_subsumption_resolution: 13
% 3.37/3.65 % res_backward_subsumption_resolution: 0
% 3.37/3.65 % res_clause_to_clause_subsumption: 45472
% 3.37/3.65 % res_orphan_elimination: 0
% 3.37/3.65 % res_tautology_del: 205
% 3.37/3.65 % res_num_eq_res_simplified: 0
% 3.37/3.65 % res_num_sel_changes: 0
% 3.37/3.65 % res_moves_from_active_to_pass: 0
% 3.37/3.65
% 3.37/3.65 % Status Unsatisfiable
% 3.37/3.65 % SZS status Unsatisfiable
% 3.37/3.65 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------