%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL806-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:45:06 PM UTC 2026
% Result : Unsatisfiable 0.71s 1.67s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_412)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_subst__subst_0,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)
| ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__subst_0) ).
cnf(cls_Suc__eq__plus1_0,axiom,
c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
cnf(cls_substn_Osimps_I2_J_0,axiom,
c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X1,X3,X4)),c_Lambda_Osubstn(X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
cnf(cls_substn__subst__n_0,axiom,
c_Lambda_Osubstn(X1,X2,X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat))),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).
cnf(cls_shift__commute_0,axiom,
hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4)),c_HOL_Ozero__class_Ozero(tc_nat)),X5) = hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X5)),c_Suc(X3)),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__commute_0) ).
cnf(cls_funpow_Osimps_I2_J_0,axiom,
c_Nat_Ocompow(c_Suc(X1),X2,X3,X3) = c_Fun_Ocomp(X2,c_Nat_Ocompow(X1,X2,X3,X3),X3,X3,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funpow_Osimps_I2_J_0) ).
cnf(cls_substn_Osimps_I3_J_0,axiom,
c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I3_J_0) ).
cnf(cls_add__eq__if_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).
cnf(cls_Suc__pred_0,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
cnf(cls_type_Osize_I4_J_0,axiom,
c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X1),X2),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Type_Otype)),c_Nat_Osize__class_Osize(X2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osize_I4_J_0) ).
cnf(cls_lift__lift_0,axiom,
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X1),X2)),c_Suc(X3)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X1),X3)),X2)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__lift_0) ).
cnf(cls_of__nat__aux_Osimps_I2_J_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,c_Suc(X3),X4,X1) = c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X3,hAPP(X2,X4),X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__aux_Osimps_I2_J_0) ).
cnf(cls_Suc__diff__diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
cnf(cls_substn_Osimps_I1_J_0,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_0) ).
cnf(cls_less__add__Suc1_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
cnf(cls_less__iff__Suc__add_1,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
cnf(cls_less__add__Suc2_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
cnf(cls_type_Osize_I2_J_0,axiom,
c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X1)),c_Type_Otype_Otype__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osize_I2_J_0) ).
cnf(cls_add__Suc_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
cnf(cls_substn_Osimps_I1_J_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
cnf(cls_Suc__less__eq_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
cnf(cls_diff__Suc__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
cnf(cls_substn__subst__0_0,axiom,
c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
cnf(cls_liftn__lift_0,axiom,
c_Lambda_Oliftn(c_Suc(X1),X2,X3) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X1,X2,X3)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
cnf(cls_substn_Osimps_I1_J_2,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
| X1 = X3
| c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
cnf(cls_add__Suc__shift_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
cnf(cls_add__Suc__right_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
cnf(cls_Suc__diff__1_0,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).
cnf(cls_Suc__pred_H_0,axiom,
( X1 = c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).
cnf(cls_Suc__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
cnf(cls_less__Suc__eq__0__disj_3,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
cnf(cls_add__is__1_4,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).
cnf(cls_one__is__add_4,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).
cnf(cls_not__less__eq_1,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
cnf(cls_less__trans__Suc_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
cnf(cls_diff__Suc__eq__diff__pred_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).
cnf(cls_diff__Suc__Suc_0,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
cnf(cls_not__less__less__Suc__eq_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
cnf(cls_less__SucE_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).
cnf(cls_less__antisym_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
cnf(cls_Suc__lessD_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
cnf(cls_Suc__lessI_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
cnf(cls_one__is__add_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).
cnf(cls_add__is__1_1,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).
cnf(cls_less__Suc0_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
cnf(cls_diff__less__Suc_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
cnf(cls_less__SucI_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
cnf(cls_one__is__add_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).
cnf(cls_one__is__add_3,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).
cnf(cls_add__is__1_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).
cnf(cls_add__is__1_3,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).
cnf(cls_add__is__1_5,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).
cnf(cls_one__is__add_5,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).
cnf(cls_of__nat__Suc_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_Oof__nat(X2,X1))
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
cnf(cls_not__less__less__Suc__eq_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
cnf(cls_not__less__eq_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
cnf(cls_one__is__add_2,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).
cnf(cls_add__is__1_2,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).
cnf(cls_less__Suc0_1,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
cnf(cls_Suc__inject_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
cnf(cls_nat_Oinject_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
cnf(cls_diff__Suc__1_0,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__1_0) ).
cnf(cls_zero__less__Suc_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
cnf(cls_gr0__conv__Suc_1,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
cnf(cls_less__Suc__eq_2,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
cnf(cls_lessI_0,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
cnf(cls_Suc__eq__plus1__left_0,axiom,
c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
cnf(cls_Suc__neq__Zero_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
cnf(cls_nat_Osimps_I3_J_0,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
cnf(cls_nat_Osimps_I2_J_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
cnf(cls_Zero__neq__Suc_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(X1) != X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
cnf(cls_n__not__Suc__n_0,axiom,
X1 != c_Suc(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(cls_One__nat__def_0,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
cnf(cls_CHAINED_0_01,axiom,
c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_bs____,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_var__app__types_0,axiom,
( X1 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X2,X1,X3,X4),X2,tc_Type_Otype,tc_Type_Otype)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB)),X1))
| ~ c_Type_Otypings(X3,X6,X7)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_0) ).
cnf(cls_var__app__types_1,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__types__1__1(X3,X4,X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
| ~ c_Type_Otypings(X1,X6,X7)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_1) ).
cnf(cls_var__app__type__eq_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB)),X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
cnf(cls_var__app__typesE_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(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(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).
cnf(cls_list__app__typeD_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
cnf(cls_list__app__typeE_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).
cnf(cls_list__app__typeI_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(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,X5)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
cnf(cls_subst__map_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X3)),X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__map_0) ).
cnf(cls_head__Var__reduction_1,axiom,
( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
cnf(cls_var__app__typesE_1,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X4,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).
cnf(cls_list__app__typeD_1,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
cnf(cls_list__app__typeE_1,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X4,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).
cnf(cls_head__Var__reduction_0,axiom,
( c_ListOrder_Ostep1(c_Lambda_Obeta,X1,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X1,X3),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
cnf(cls_apps__preserves__betas_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X2,X3,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
cnf(cls_apps__preserves__beta2_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
cnf(cls_apps__preserves__beta_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
cnf(cls_CHAINED_0,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_Cons_I3_J_0,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_I3_J_0) ).
cnf(cls_Beta_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,X2))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).
cnf(cls_varT_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),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)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_varT_0) ).
cnf(cls_nT_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nT_0) ).
cnf(cls_Var_I2_J_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I2_J_0) ).
cnf(cls_uT_H_0,axiom,
hBOOL(hAPP(hAPP(hAPP(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)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_H_0) ).
cnf(cls_lift__map_0,axiom,
hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X3),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__map_0) ).
cnf(cls_substs__lemma_0,axiom,
( c_Type_Otypings(X1,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X2)),X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X3),X6),X4,X5)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substs__lemma_0) ).
cnf(cls_fcomp__assoc_0,axiom,
c_Fun_Ofcomp(c_Fun_Ofcomp(X1,X2,X3,X4,X5),X6,X3,X5,X7) = c_Fun_Ofcomp(X1,c_Fun_Ofcomp(X2,X6,X4,X5,X7),X3,X4,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__assoc_0) ).
cnf(cls_o__assoc_0,axiom,
c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
cnf(cls_headT_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),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))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_headT_0) ).
cnf(cls_typing__elims_I2_J_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X2,X4)),X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).
cnf(cls_comp__cong_0,axiom,
( hAPP(c_Fun_Ocomp(X1,X2,X7,X8,X9),X3) = hAPP(c_Fun_Ocomp(X4,X5,X10,X8,X11),X6)
| hAPP(X1,hAPP(X2,X3)) != hAPP(X4,hAPP(X5,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
cnf(cls_IT_OVar_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X2,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
cnf(cls_typing__elims_I3_J_1,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(X2,X1,X3))),X3),c_Type_Osko__Type__Xtyping__elims__3__2(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X3)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_1) ).
cnf(cls_subst__lemma_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X3)),X5),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
cnf(cls_o__eq__dest_0,axiom,
( hAPP(X1,hAPP(X2,X9)) = hAPP(X6,hAPP(X7,X9))
| c_Fun_Ocomp(X1,X2,X3,X4,X5) != c_Fun_Ocomp(X6,X7,X8,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
cnf(cls_o__eq__id__dest_0,axiom,
( hAPP(X1,hAPP(X2,X7)) = hAPP(X6,X7)
| c_Fun_Ocomp(X1,X2,X3,X4,X5) != c_Fun_Ocomp(c_Fun_Oid(X4),X6,X4,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).
cnf(cls_Abs__apps__eq__Abs__apps__conv_0,axiom,
( X1 = X3
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
cnf(cls_Var__apps__eq__Var__apps__conv_0,axiom,
( X1 = X3
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
cnf(cls_Abs__apps__eq__Abs__apps__conv_1,axiom,
( X2 = X4
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
cnf(cls_Var__apps__eq__Var__apps__conv_1,axiom,
( X2 = X4
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
cnf(cls_foldl__assoc_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
cnf(cls_Var__apps__neq__Abs__apps_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
cnf(cls_apps__eq__tail__conv_0,axiom,
( X1 = X3
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
cnf(cls_foldl__absorb0_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
cnf(cls_foldl__foldr1__lemma_0,axiom,
( 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).
cnf(cls_MI1_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X5)))
| v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X1),X2)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X6),X4),X1))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X6),X5),X1)),X3),X7))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI1_0) ).
cnf(cls_MI2_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X5)))
| v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X1),X2)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X6),X4),X2))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X6),X5),X2)),X3),X7))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI2_0) ).
cnf(cls_CHAINED_0_02,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X1),X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X3),X2),v_T____)),v_b____),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
cnf(cls_Cons_I1_J_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X1),X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X3),X2),v_T____)),v_b____),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_I1_J_0) ).
cnf(cls_map__map_0,axiom,
c_List_Omap(X1,c_List_Omap(X2,X3,X4,X5),X5,X6) = c_List_Omap(c_Fun_Ocomp(X1,X2,X5,X6,X4),X3,X4,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__map_0) ).
cnf(cls_Abs_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),hAPP(hAPP(c_Type_Otype_OFun,X3),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X3)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).
cnf(cls_abs__typeE_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2))),X2),c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__typeE_0) ).
cnf(cls_K__record__comp_0,axiom,
hAPP(c_Fun_Ocomp(c_COMBK(X1,X2,X3),X4,X3,X2,t_a),v_x) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_K__record__comp_0) ).
cnf(cls_CHAINED_1,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__CHAINED__1(v_T____,v_b____,v_e____,v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
cnf(cls_Cons_I1_J_1,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__1__1(v_T____,v_b____,v_e____,v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_I1_J_1) ).
cnf(cls_Cons_Ohyps_I1_J_1,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_b____,v_e____,v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_Ohyps_I1_J_1) ).
cnf(cls_funpow__add_0,axiom,
c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,X4,X4) = c_Fun_Ocomp(c_Nat_Ocompow(X1,X3,X4,X4),c_Nat_Ocompow(X2,X3,X4,X4),X4,X4,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funpow__add_0) ).
cnf(cls_fcomp__apply_0,axiom,
hAPP(c_Fun_Ofcomp(X1,X2,X3,X4,X5),X6) = hAPP(X2,hAPP(X1,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__apply_0) ).
cnf(cls_o__apply_0,axiom,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).
cnf(cls_o__eq__dest__lhs_0,axiom,
hAPP(X1,hAPP(X2,X3)) = hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
cnf(cls_fcomp__def_0,axiom,
hAPP(c_Fun_Ofcomp(X1,X2,t_a,X3,X4),v_x) = hAPP(X2,hAPP(X1,v_x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__def_0) ).
cnf(cls_o__def_0,axiom,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,t_a),v_x) = hAPP(X1,hAPP(X2,v_x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__def_0) ).
cnf(cls_foldl__foldr1_0,axiom,
( 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).
cnf(cls_foldr__conv__foldl_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__conv__foldl_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)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_T_0) ).
cnf(cls_lift__type_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),X3)),hAPP(hAPP(c_Lambda_Olift,X4),X2)),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).
cnf(cls_Abs__App__neq__Var__apps_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
cnf(cls_Abs__eq__apps__conv_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
cnf(cls_Var__eq__apps__conv_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
cnf(cls_apps__eq__Abs__conv_0,axiom,
( X1 = c_Lambda_OdB_OAbs(X3)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
cnf(cls_lift__subst_0,axiom,
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),X4) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X2),X4)),X3)
| ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst_0) ).
cnf(cls_typing__elims_I2_J_1,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X4,X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).
cnf(cls_lift__types_0,axiom,
( c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),X3),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X2),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(X1,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__types_0) ).
cnf(cls_argT_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_T_H_H____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_argT_0) ).
cnf(cls_conjecture_0,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_funpow__swap1_0,axiom,
hAPP(X1,hAPP(c_Nat_Ocompow(X2,X1,X3,X3),X4)) = hAPP(c_Nat_Ocompow(X2,X1,X3,X3),hAPP(X1,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funpow__swap1_0) ).
cnf(cls_lifts__IT_0,axiom,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lifts__IT_0) ).
cnf(cls_subst__preserves__beta2_H_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
cnf(cls_subst__preserves__beta_H_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X4),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
cnf(cls_subst__preserves__beta2_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
cnf(cls_App_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,X5),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).
cnf(cls_lift__subst__lt_0,axiom,
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),X4) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X4)),hAPP(hAPP(c_Lambda_Olift,X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).
cnf(cls_subst__preserves__beta_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X4),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
cnf(cls_id__fcomp_0,axiom,
c_Fun_Ofcomp(c_Fun_Oid(X1),X2,X1,X1,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__fcomp_0) ).
cnf(cls_id__o_0,axiom,
c_Fun_Ocomp(c_Fun_Oid(X1),X2,X1,X1,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__o_0) ).
cnf(cls_fcomp__id_0,axiom,
c_Fun_Ofcomp(X1,c_Fun_Oid(X2),X3,X2,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__id_0) ).
cnf(cls_o__id_0,axiom,
c_Fun_Ocomp(X1,c_Fun_Oid(X2),X2,X3,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__id_0) ).
cnf(cls_rtrancl__beta__App_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).
cnf(cls_nat__diff__split_1,axiom,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X2,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).
cnf(cls_nat__diff__split__asm_1,axiom,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X2,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).
cnf(cls_subst__App_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
cnf(cls_lift__preserves__beta_H_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X2)),hAPP(hAPP(c_Lambda_Olift,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).
cnf(cls_rtrancl__beta__AppR_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
cnf(cls_rtrancl__beta__AppL_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
cnf(cls_semiring__1__class_Oof__nat__code_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(X2,X1) = c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(X1,X1,X1),c_HOL_Oplus__class_Oplus(X1)),c_HOL_Oone__class_Oone(X1)),X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semiring__1__class_Oof__nat__code_0) ).
cnf(cls_beta_0,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
cnf(cls_subst__Abs_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X1)),X2),X3) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
cnf(cls_rtranclp__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_subject__reduction_H_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
cnf(cls_typing__elims_I3_J_0,axiom,
( X1 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X1,X2,X3)),c_Type_Osko__Type__Xtyping__elims__3__2(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),c_Lambda_OdB_OAbs(X3)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_0) ).
cnf(cls_lift__preserves__beta_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X2)),hAPP(hAPP(c_Lambda_Olift,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
cnf(cls_appR_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
cnf(cls_appL_0,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
cnf(cls_converse__rtranclp__into__rtranclp_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X5),X4))
| ~ hBOOL(hAPP(hAPP(X1,X3),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
cnf(cls_rtranclp_Ortrancl__into__rtrancl_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
cnf(cls_subject__reduction_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X4),X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
cnf(cls_conjecture_3,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_nat__diff__split_0,axiom,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
cnf(cls_liftn_Osimps_I2_J_0,axiom,
c_Lambda_Oliftn(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X1,X2,X4)),c_Lambda_Oliftn(X1,X3,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
cnf(cls_add__less__cancel__right_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
cnf(cls_add__less__cancel__left_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
cnf(cls_subst__Var__IT_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
cnf(cls_rtrancl__beta__Abs_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)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
cnf(cls_shift__lt_0,axiom,
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X5) = hAPP(X2,c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X3,X5,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__lt_0) ).
cnf(cls_add__strict__mono_0,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),X5),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
cnf(cls_lift_Osimps_I2_J_0,axiom,
hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
cnf(cls_diff__less__mono2_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
cnf(cls_nat__add__left__cancel__less_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
cnf(cls_comm__monoid__add_Omult__assoc_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_class__semiring_Oadd__a_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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(cls_add__less__mono_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
cnf(cls_less__diff__conv_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
cnf(cls_add__cancel__21_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) = X5
| ~ 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),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
cnf(cls_less__diff__conv_1,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
cnf(cls_subst__lift_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X2)),X3),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
cnf(cls_liftn_Osimps_I3_J_0,axiom,
c_Lambda_Oliftn(X1,c_Lambda_OdB_OAbs(X2),X3) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).
cnf(cls_nat__add__assoc_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
cnf(cls_add__neg__neg_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
cnf(cls_add__pos__pos_0,axiom,
( 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)
| ~ 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
cnf(cls_add__less__cancel__left_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)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
cnf(cls_add__strict__left__mono_0,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)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
cnf(cls_add__less__cancel__right_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)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
cnf(cls_add__strict__right__mono_0,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)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
cnf(cls_pos__add__strict_0,axiom,
( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
cnf(cls_add__gr__0_0,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(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
cnf(cls_shift__gt_0,axiom,
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X5) = hAPP(X2,X5)
| ~ c_HOL_Oord__class_Oless(X5,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).
cnf(cls_diff__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat)
| ~ 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(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).
cnf(cls_typing__elims_I1_J_0,axiom,
( hAPP(X1,X2) = X3
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
cnf(cls_less__iff__diff__less__0_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
cnf(cls_even__less__0__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
cnf(cls_less__eqI_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
cnf(cls_less__eqI_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
cnf(cls_nat__add__left__cancel__less_1,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
cnf(cls_add__less__mono1_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
cnf(cls_lift_Osimps_I3_J_0,axiom,
hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X1)),X2) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
cnf(cls_comm__monoid__add_Omult__left__commute_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_add__cancel__21_1,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
cnf(cls_r__into__rtranclp_0,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
cnf(cls_diff__commute_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
cnf(cls_subst__Var_0,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_0) ).
cnf(cls_subst__gt_0,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__gt_0) ).
cnf(cls_zero__less__diff_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
cnf(cls_diff__diff__left_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
cnf(cls_diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
cnf(cls_diff__cancel2_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
cnf(cls_less__add__eq__less_0,axiom,
( c_HOL_Oord__class_Oless(X1,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
cnf(cls_add__lessD1_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
cnf(cls_diff__add__cancel_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(cls_nat__add__left__commute_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
cnf(cls_even__less__0__iff_1,axiom,
( 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_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
( 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_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
( 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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
cnf(cls_less__iff__diff__less__0_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
cnf(cls_of__nat__aux_Osimps_I1_J_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,c_HOL_Ozero__class_Ozero(tc_nat),X3,X1) = X3
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__aux_Osimps_I1_J_0) ).
cnf(cls_funpow_Osimps_I1_J_0,axiom,
c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2,X2) = c_Fun_Oid(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funpow_Osimps_I1_J_0) ).
cnf(cls_typing_OVar_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),hAPP(X1,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
cnf(cls_shift__eq_0,axiom,
hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X3) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
cnf(cls_zero__less__diff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
cnf(cls_of__nat__add_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1)),c_Nat_Osemiring__1__class_Oof__nat(X3,X1))
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
cnf(cls_less__imp__diff__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
cnf(cls_app__Var__IT_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)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
cnf(cls_argsT_0,axiom,
c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____),v_as____,v_Ts____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_argsT_0) ).
cnf(cls_add__gr__0_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
cnf(cls_add__gr__0_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
cnf(cls_order__less__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
cnf(cls_xt1_I10_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
cnf(cls_abs_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)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
cnf(cls_of__nat__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
cnf(cls_termination__basic__simps_I1_J_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
cnf(cls_trans__less__add1_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
cnf(cls_termination__basic__simps_I2_J_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
cnf(cls_trans__less__add2_0,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
cnf(cls_not__add__less1_0,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
cnf(cls_not__add__less2_0,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
cnf(cls_lift__IT_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
cnf(cls_liftn_Osimps_I1_J_1,axiom,
( c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X3) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1))
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
cnf(cls_zero__less__two_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
cnf(cls_add__diff__inverse_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
cnf(cls_lift_Osimps_I1_J_1,axiom,
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
cnf(cls_of__nat__0__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
cnf(cls_subst__lt_0,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).
cnf(cls_of__nat__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
cnf(cls_nat__less__cases_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
cnf(cls_rtranclp_Ortrancl__refl_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
cnf(cls_Nitpick_Ortranclp__def_1,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
cnf(cls_of__nat__0__less__iff_1,axiom,
( 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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
cnf(cls_eq__eqI_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
cnf(cls_eq__eqI_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
cnf(cls_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
cnf(cls_diffs0__imp__equal_0,axiom,
( X2 = X1
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
cnf(cls_less__add__one_0,axiom,
( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
cnf(cls_add__right__cancel_0,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
cnf(cls_add__left__cancel_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
cnf(cls_add__imp__eq_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
cnf(cls_subst__Var_2,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(X1)
| X1 = X3
| c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).
cnf(cls_add__diff__cancel_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
cnf(cls_subst__Var_1,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).
cnf(cls_beta__cases_I1_J_0,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
cnf(cls_uT_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).
cnf(cls_conjecture_2,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Var_I4_J_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I4_J_0) ).
cnf(cls_liftn_Osimps_I1_J_0,axiom,
( c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X3) = c_Lambda_OdB_OVar(X2)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
cnf(cls_nat__add__right__cancel_0,axiom,
( X1 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
cnf(cls_nat__add__left__cancel_0,axiom,
( X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
cnf(cls_natgb_Oadd__cancel_0,axiom,
( X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
cnf(cls_diff__add__0_0,axiom,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
cnf(cls_diff__add__inverse_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
cnf(cls_diff__add__inverse2_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
cnf(cls_of__nat__less__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
cnf(cls_lift_Osimps_I1_J_0,axiom,
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
cnf(cls_linorder__less__linear_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
cnf(cls_linorder__neqE_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X3,X2,X1)
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
cnf(cls_type_Osimps_I2_J_0,axiom,
( X1 = X3
| hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != hAPP(hAPP(c_Type_Otype_OFun,X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
cnf(cls_dB_Osimps_I2_J_0,axiom,
( X1 = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
cnf(cls_type_Osimps_I2_J_1,axiom,
( X2 = X4
| hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != hAPP(hAPP(c_Type_Otype_OFun,X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
cnf(cls_dB_Osimps_I2_J_1,axiom,
( X2 = X4
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
cnf(cls_not__one__less__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
cnf(cls_comm__monoid__add_Omult__commute_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_class__semiring_Oadd__c_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_subst__eq_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
cnf(cls_linorder__neqE__nat_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
cnf(cls_nat__neq__iff_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
cnf(cls_class__ringb_Osubr0__iff_0,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
cnf(cls_eq__iff__diff__eq__0_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
cnf(cls_right__minus__eq_0,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
cnf(cls_double__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
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),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
cnf(cls_nat__add__commute_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
cnf(cls_gr__implies__not0_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
cnf(cls_not__less0_0,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
cnf(cls_less__not__refl_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
cnf(cls_nat__less__le_1,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
cnf(cls_Lambda_0,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
cnf(cls_double__eq__0__iff_1,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
cnf(cls_add__is__0_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
cnf(cls_add__is__0_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
cnf(cls_add__eq__self__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
cnf(cls_natgb_Oadd__r0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
cnf(cls_zero__less__one_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
cnf(cls_class__ringb_Osubr0__iff_1,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
cnf(cls_comm__monoid__add_Omult__1_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
cnf(cls_class__semiring_Osemiring__rules_I5_J_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
cnf(cls_class__semiring_Oadd__0_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
cnf(cls_add__0__left_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
cnf(cls_diff__0__right_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
cnf(cls_right__minus__eq_1,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
cnf(cls_diff__self_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).
cnf(cls_dB_Osimps_I8_J_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
cnf(cls_dB_Osimps_I5_J_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
cnf(cls_dB_Osimps_I9_J_0,axiom,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
cnf(cls_dB_Osimps_I4_J_0,axiom,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
cnf(cls_gr0I_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
cnf(cls_diff__0__eq__0_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
cnf(cls_liftn__0_0,axiom,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).
cnf(cls_add__is__0_2,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).
cnf(cls_minus__nat_Odiff__0_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
cnf(cls_diff__self__eq__0_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
c_fequal(X1,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_rtranclp__idemp_0,axiom,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2) = c_Transitive__Closure_Ortranclp(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
cnf(cls_of__nat__eq__iff_0,axiom,
( X2 = X3
| ~ class_Nat_Osemiring__char__0(X1)
| c_Nat_Osemiring__1__class_Oof__nat(X2,X1) != c_Nat_Osemiring__1__class_Oof__nat(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
cnf(cls_plus__nat_Oadd__0_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
cnf(cls_Nat_Oadd__0__right_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
cnf(cls_natgb_Oadd__r0__iff_1,axiom,
X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
cnf(cls_Var__IT_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
cnf(clsarity_fun__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
cnf(cls_of__nat__1_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
cnf(cls_of__nat__0_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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
cnf(cls_conjecture_1,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Var_I3_J_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).
cnf(cls_uIT_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).
cnf(cls_id__apply_0,axiom,
hAPP(c_Fun_Oid(X1),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).
cnf(cls_zero__neq__one_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
cnf(cls_one__neq__zero_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
cnf(cls_id__def_0,axiom,
hAPP(c_Fun_Oid(t_a),v_x) = v_x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__def_0) ).
cnf(cls_dB_Osimps_I3_J_0,axiom,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
cnf(cls_dB_Osimps_I1_J_0,axiom,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
cnf(cls_dB_Osimps_I7_J_0,axiom,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
cnf(cls_dB_Osimps_I6_J_0,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
cnf(cls_True_0,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).
cnf(i_0_411,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),c_Suc(X4))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)
| ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
cls_subst__subst_0 ).
cnf(i_0_412,axiom,
c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
cls_Suc__eq__plus1_0 ).
cnf(i_0_413,axiom,
c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3,X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(X1,X3,X4)),c_Lambda_Osubstn(X2,X3,X4)),
cls_substn_Osimps_I2_J_0 ).
cnf(i_0_414,axiom,
c_Lambda_Osubstn(X1,X2,X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat))),X3),
cls_substn__subst__n_0 ).
cnf(i_0_415,axiom,
hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4)),c_HOL_Ozero__class_Ozero(tc_nat)),X5) = hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X5)),c_Suc(X3)),X4),
cls_shift__commute_0 ).
cnf(i_0_416,axiom,
c_Nat_Ocompow(c_Suc(X1),X2,X3,X3) = c_Fun_Ocomp(X2,c_Nat_Ocompow(X1,X2,X3,X3),X3,X3,X3),
cls_funpow_Osimps_I2_J_0 ).
cnf(i_0_417,axiom,
c_Lambda_Osubstn(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
cls_substn_Osimps_I3_J_0 ).
cnf(i_0_418,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2))
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_add__eq__if_1 ).
cnf(i_0_419,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_Suc__pred_0 ).
cnf(i_0_420,axiom,
c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X1),X2),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Type_Otype)),c_Nat_Osize__class_Osize(X2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
cls_type_Osize_I4_J_0 ).
cnf(i_0_421,axiom,
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X1),X2)),c_Suc(X3)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X1),X3)),X2)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
cls_lift__lift_0 ).
cnf(i_0_422,axiom,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,c_Suc(X3),X4,X1) = c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X3,hAPP(X2,X4),X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_of__nat__aux_Osimps_I2_J_0 ).
cnf(i_0_423,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
cls_Suc__diff__diff_0 ).
cnf(i_0_424,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
cls_substn_Osimps_I1_J_0 ).
cnf(i_0_425,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
cls_less__add__Suc1_0 ).
cnf(i_0_426,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
cls_less__iff__Suc__add_1 ).
cnf(i_0_427,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),tc_nat),
cls_less__add__Suc2_0 ).
cnf(i_0_428,axiom,
c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X1)),c_Type_Otype_Otype__size(X2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
cls_type_Osize_I2_J_0 ).
cnf(i_0_429,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
cls_add__Suc_0 ).
cnf(i_0_430,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_substn_Osimps_I1_J_1 ).
cnf(i_0_431,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
cls_Suc__less__eq_0 ).
cnf(i_0_432,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_diff__Suc__less_0 ).
cnf(i_0_433,axiom,
c_Lambda_Osubstn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),
cls_substn__subst__0_0 ).
cnf(i_0_434,axiom,
c_Lambda_Oliftn(c_Suc(X1),X2,X3) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X1,X2,X3)),X3),
cls_liftn__lift_0 ).
cnf(i_0_435,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(X1),X2,X3) = c_Lambda_OdB_OVar(X1)
| X1 = X3
| c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
cls_substn_Osimps_I1_J_2 ).
cnf(i_0_436,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)),
cls_add__Suc__shift_0 ).
cnf(i_0_437,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Suc(X2)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
cls_add__Suc__right_0 ).
cnf(i_0_438,axiom,
( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_Suc__diff__1_0 ).
cnf(i_0_439,axiom,
( X1 = c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_Suc__pred_H_0 ).
cnf(i_0_440,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_Suc__mono_0 ).
cnf(i_0_441,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_less__Suc__eq__0__disj_3 ).
cnf(i_0_442,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
cls_add__is__1_4 ).
cnf(i_0_443,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
cls_one__is__add_4 ).
cnf(i_0_444,axiom,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
cls_not__less__eq_1 ).
cnf(i_0_445,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_less__trans__Suc_0 ).
cnf(i_0_446,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
cls_diff__Suc__eq__diff__pred_0 ).
cnf(i_0_447,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
cls_diff__Suc__Suc_0 ).
cnf(i_0_448,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
cls_not__less__less__Suc__eq_0 ).
cnf(i_0_449,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
cls_less__SucE_0 ).
cnf(i_0_450,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
cls_less__antisym_0 ).
cnf(i_0_451,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
cls_Suc__lessD_0 ).
cnf(i_0_452,axiom,
( c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat)
| c_Suc(X1) = X2
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_Suc__lessI_0 ).
cnf(i_0_453,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
cls_one__is__add_1 ).
cnf(i_0_454,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_add__is__1_1 ).
cnf(i_0_455,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
cls_less__Suc0_0 ).
cnf(i_0_456,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
cls_diff__less__Suc_0 ).
cnf(i_0_457,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_less__SucI_0 ).
cnf(i_0_458,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
cls_one__is__add_0 ).
cnf(i_0_459,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
cls_one__is__add_3 ).
cnf(i_0_460,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_add__is__1_0 ).
cnf(i_0_461,axiom,
( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_add__is__1_3 ).
cnf(i_0_462,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
cls_add__is__1_5 ).
cnf(i_0_463,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
cls_one__is__add_5 ).
cnf(i_0_464,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_Oof__nat(X2,X1))
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_of__nat__Suc_0 ).
cnf(i_0_465,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
cls_not__less__less__Suc__eq_1 ).
cnf(i_0_466,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
cls_not__less__eq_0 ).
cnf(i_0_467,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
cls_one__is__add_2 ).
cnf(i_0_468,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
cls_add__is__1_2 ).
cnf(i_0_469,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
cls_less__Suc0_1 ).
cnf(i_0_470,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
cls_Suc__inject_0 ).
cnf(i_0_471,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
cls_nat_Oinject_0 ).
cnf(i_0_472,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
cls_diff__Suc__1_0 ).
cnf(i_0_473,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
cls_zero__less__Suc_0 ).
cnf(i_0_474,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
cls_gr0__conv__Suc_1 ).
cnf(i_0_475,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
cls_less__Suc__eq_2 ).
cnf(i_0_476,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
cls_lessI_0 ).
cnf(i_0_477,axiom,
c_Suc(X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1),
cls_Suc__eq__plus1__left_0 ).
cnf(i_0_478,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
cls_Suc__neq__Zero_0 ).
cnf(i_0_479,axiom,
c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
cls_nat_Osimps_I3_J_0 ).
cnf(i_0_480,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
cls_nat_Osimps_I2_J_0 ).
cnf(i_0_481,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
cls_Zero__neq__Suc_0 ).
cnf(i_0_482,axiom,
c_Suc(X1) != X1,
cls_Suc__n__not__n_0 ).
cnf(i_0_483,axiom,
X1 != c_Suc(X1),
cls_n__not__Suc__n_0 ).
cnf(i_0_484,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
cls_One__nat__def_0 ).
cnf(i_0_485,axiom,
c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_bs____,tc_Lambda_OdB),
cls_CHAINED_0_01,
[final] ).
cnf(i_0_486,axiom,
( X1 = c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X2,X1,X3,X4),X2,tc_Type_Otype,tc_Type_Otype)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB)),X1))
| ~ c_Type_Otypings(X3,X6,X7)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X2)) ),
cls_var__app__types_0,
[final] ).
cnf(i_0_487,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__types__1__1(X3,X4,X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB)),X4))
| ~ c_Type_Otypings(X1,X6,X7)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X5),X6,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
cls_var__app__types_1,
[final] ).
cnf(i_0_488,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB)),X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB)),X1)) ),
cls_var__app__type__eq_0,
[final] ).
cnf(i_0_489,axiom,
( hBOOL(hAPP(hAPP(hAPP(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(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
cls_var__app__typesE_0,
[final] ).
cnf(i_0_490,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
cls_list__app__typeD_0,
[final] ).
cnf(i_0_491,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
cls_list__app__typeE_0,
[final] ).
cnf(i_0_492,axiom,
( hBOOL(hAPP(hAPP(hAPP(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,X5)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype))) ),
cls_list__app__typeI_0,
[final] ).
cnf(i_0_493,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X3)),X4),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
cls_subst__map_0,
[final] ).
cnf(i_0_494,axiom,
( X1 = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X3,X1),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB)),X1)) ),
cls_head__Var__reduction_1,
[final] ).
cnf(i_0_495,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X4,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
cls_var__app__typesE_1,
[final] ).
cnf(i_0_496,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
cls_list__app__typeD_1,
[final] ).
cnf(i_0_497,axiom,
( c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X4,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
cls_list__app__typeE_1,
[final] ).
cnf(i_0_498,axiom,
( c_ListOrder_Ostep1(c_Lambda_Obeta,X1,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X1,X3),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
cls_head__Var__reduction_0,
[final] ).
cnf(i_0_499,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X2,X3,tc_Lambda_OdB) ),
cls_apps__preserves__betas_0,
[final] ).
cnf(i_0_500,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
cls_apps__preserves__beta2_0,
[final] ).
cnf(i_0_501,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
cls_apps__preserves__beta_0,
[final] ).
cnf(i_0_502,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
cls_CHAINED_0,
[final] ).
cnf(i_0_503,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
cls_Cons_I3_J_0,
[final] ).
cnf(i_0_504,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,X2))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_Lambda_OdB,tc_Lambda_OdB))) ),
cls_Beta_0,
[final] ).
cnf(i_0_505,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),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)))),
cls_varT_0,
[final] ).
cnf(i_0_506,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
cls_nT_0,
[final] ).
cnf(i_0_507,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)),
cls_Var_I2_J_0,
[final] ).
cnf(i_0_508,axiom,
hBOOL(hAPP(hAPP(hAPP(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)))),
cls_uT_H_0,
[final] ).
cnf(i_0_509,axiom,
hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X3),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
cls_lift__map_0,
[final] ).
cnf(i_0_510,axiom,
( c_Type_Otypings(X1,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X2)),X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X3),X6),X4,X5)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X6)) ),
cls_substs__lemma_0,
[final] ).
cnf(i_0_511,axiom,
c_Fun_Ofcomp(c_Fun_Ofcomp(X1,X2,X3,X4,X5),X6,X3,X5,X7) = c_Fun_Ofcomp(X1,c_Fun_Ofcomp(X2,X6,X4,X5,X7),X3,X4,X7),
cls_fcomp__assoc_0,
[final] ).
cnf(i_0_512,axiom,
c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
cls_o__assoc_0,
[final] ).
cnf(i_0_513,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),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))),
cls_headT_0,
[final] ).
cnf(i_0_514,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X2,X4)),X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4)),X3)) ),
cls_typing__elims_I2_J_0,
[final] ).
cnf(i_0_515,axiom,
( hAPP(c_Fun_Ocomp(X1,X2,X7,X8,X9),X3) = hAPP(c_Fun_Ocomp(X4,X5,X10,X8,X11),X6)
| hAPP(X1,hAPP(X2,X3)) != hAPP(X4,hAPP(X5,X6)) ),
cls_comp__cong_0,
[final] ).
cnf(i_0_516,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X2,tc_Lambda_OdB) ),
cls_IT_OVar_0,
[final] ).
cnf(i_0_517,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(X2,X1,X3))),X3),c_Type_Osko__Type__Xtyping__elims__3__2(X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X3)),X2)) ),
cls_typing__elims_I3_J_1,
[final] ).
cnf(i_0_518,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X3) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X5),X3)),X2),X4)
| ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(rw,[status(thm)],[i_0_411,c_0_412]),
[final] ).
cnf(i_0_519,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4)),X6))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X4),X3)),X5),X6)) ),
cls_subst__lemma_0,
[final] ).
cnf(i_0_520,axiom,
( hAPP(X1,hAPP(X2,X9)) = hAPP(X6,hAPP(X7,X9))
| c_Fun_Ocomp(X1,X2,X3,X4,X5) != c_Fun_Ocomp(X6,X7,X8,X4,X5) ),
cls_o__eq__dest_0,
[final] ).
cnf(i_0_521,axiom,
( hAPP(X1,hAPP(X2,X7)) = hAPP(X6,X7)
| c_Fun_Ocomp(X1,X2,X3,X4,X5) != c_Fun_Ocomp(c_Fun_Oid(X4),X6,X4,X4,X5) ),
cls_o__eq__id__dest_0,
[final] ).
cnf(i_0_522,axiom,
( X1 = X3
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_Abs__apps__eq__Abs__apps__conv_0,
[final] ).
cnf(i_0_523,axiom,
( X1 = X3
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_Var__apps__eq__Var__apps__conv_0,
[final] ).
cnf(i_0_524,axiom,
( X2 = X4
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_Abs__apps__eq__Abs__apps__conv_1,
[final] ).
cnf(i_0_525,axiom,
( X2 = X4
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_Var__apps__eq__Var__apps__conv_1,
[final] ).
cnf(i_0_526,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) ),
cls_foldl__assoc_0,
[final] ).
cnf(i_0_527,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
cls_Var__apps__neq__Abs__apps_0,
[final] ).
cnf(i_0_528,axiom,
( X1 = X3
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
cls_apps__eq__tail__conv_0,
[final] ).
cnf(i_0_529,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) ),
cls_foldl__absorb0_0,
[final] ).
cnf(i_0_530,axiom,
( 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) ),
cls_foldl__foldr1__lemma_0,
[final] ).
cnf(i_0_531,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X5)))
| v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X1),X2)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X6),X4),X1))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X6),X5),X1)),X3),X7))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
cls_MI1_0,
[final] ).
cnf(i_0_532,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X3),X4),X5)))
| v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X1),X2)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X6),X4),X2))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X6),X5),X2)),X3),X7))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X3)) ),
cls_MI2_0,
[final] ).
cnf(i_0_533,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X1),X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X3),X2),v_T____)),v_b____),X4)) ),
cls_CHAINED_0_02,
[final] ).
cnf(i_0_534,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X1),X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X3),X1),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X3),X2),v_T____)),v_b____),X4)) ),
cls_Cons_I1_J_0,
[final] ).
cnf(i_0_535,axiom,
c_List_Omap(X1,c_List_Omap(X2,X3,X4,X5),X5,X6) = c_List_Omap(c_Fun_Ocomp(X1,X2,X5,X6,X4),X3,X4,X6),
cls_map__map_0,
[final] ).
cnf(i_0_536,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),hAPP(hAPP(c_Type_Otype_OFun,X3),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X3)),X2),X4)) ),
cls_Abs_0,
[final] ).
cnf(i_0_537,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(X1,X2))),X2),c_Type_Osko__Type__Xabs__typeE__1__2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OAbs(X2)),X3)) ),
cls_abs__typeE_0,
[final] ).
cnf(i_0_538,axiom,
hAPP(c_Fun_Ocomp(c_COMBK(X1,X2,X3),X4,X3,X2,t_a),v_x) = X1,
cls_K__record__comp_0,
[final] ).
cnf(i_0_539,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__CHAINED__1(v_T____,v_b____,v_e____,v_i____))),
cls_CHAINED_1,
[final] ).
cnf(i_0_540,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__1__1(v_T____,v_b____,v_e____,v_i____))),
cls_Cons_I1_J_1,
[final] ).
cnf(i_0_541,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_b____,v_e____,v_i____))),
cls_Cons_Ohyps_I1_J_1,
[final] ).
cnf(i_0_542,axiom,
c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,X4,X4) = c_Fun_Ocomp(c_Nat_Ocompow(X1,X3,X4,X4),c_Nat_Ocompow(X2,X3,X4,X4),X4,X4,X4),
cls_funpow__add_0,
[final] ).
cnf(i_0_543,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),c_Lambda_Oliftn(X4,X3,c_HOL_Ozero__class_Ozero(tc_nat))),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Oliftn(X4,X3,c_HOL_Ozero__class_Ozero(tc_nat))),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),c_Lambda_Oliftn(X4,X3,c_HOL_Ozero__class_Ozero(tc_nat))),X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_413,c_0_414]),c_0_414]),c_0_414]),
[final] ).
cnf(i_0_544,axiom,
hAPP(c_Fun_Ofcomp(X1,X2,X3,X4,X5),X6) = hAPP(X2,hAPP(X1,X6)),
cls_fcomp__apply_0,
[final] ).
cnf(i_0_545,axiom,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_o__apply_0,
[final] ).
cnf(i_0_546,axiom,
hAPP(X1,hAPP(X2,X3)) = hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3),
cls_o__eq__dest__lhs_0,
[final] ).
cnf(i_0_547,axiom,
hAPP(c_Fun_Ofcomp(X1,X2,t_a,X3,X4),v_x) = hAPP(X2,hAPP(X1,v_x)),
cls_fcomp__def_0,
[final] ).
cnf(i_0_548,axiom,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,t_a),v_x) = hAPP(X1,hAPP(X2,v_x)),
cls_o__def_0,
[final] ).
cnf(i_0_549,axiom,
( 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) ),
cls_foldl__foldr1_0,
[final] ).
cnf(i_0_550,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) ),
cls_foldr__conv__foldl_0,
[final] ).
cnf(i_0_551,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)),
cls_T_0,
[final] ).
cnf(i_0_552,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),X3)),hAPP(hAPP(c_Lambda_Olift,X4),X2)),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X5)) ),
cls_lift__type_0,
[final] ).
cnf(i_0_553,plain,
hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4)),c_HOL_Ozero__class_Ozero(tc_nat)),X5) = hAPP(hAPP(hAPP(c_Type_Oshift(X1),hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat))),X4),
inference(rw,[status(thm)],[i_0_415,c_0_412]),
[final] ).
cnf(i_0_554,plain,
c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,X3,X3) = c_Fun_Ocomp(X2,c_Nat_Ocompow(X1,X2,X3,X3),X3,X3,X3),
inference(rw,[status(thm)],[i_0_416,c_0_412]),
[final] ).
cnf(i_0_555,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB),
cls_Abs__App__neq__Var__apps_0,
[final] ).
cnf(i_0_556,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X1)),c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat))),X3) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X2,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_417,c_0_414]),c_0_414]),
[final] ).
cnf(i_0_557,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) ),
cls_Abs__eq__apps__conv_0,
[final] ).
cnf(i_0_558,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) ),
cls_Var__eq__apps__conv_0,
[final] ).
cnf(i_0_559,axiom,
( X1 = c_Lambda_OdB_OAbs(X3)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X3) ),
cls_apps__eq__Abs__conv_0,
[final] ).
cnf(i_0_560,axiom,
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),X4) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X2),X4)),X3)
| ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
cls_lift__subst_0,
[final] ).
cnf(i_0_561,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X4,X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2)),X3)) ),
cls_typing__elims_I2_J_1,
[final] ).
cnf(i_0_562,axiom,
( c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X1),X2),X3),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X2),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)
| ~ c_Type_Otypings(X1,X4,X5) ),
cls_lift__types_0,
[final] ).
cnf(i_0_563,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_T_H_H____)),
cls_argT_0,
[final] ).
cnf(i_0_564,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
cls_conjecture_0,
[final] ).
cnf(i_0_565,axiom,
hAPP(X1,hAPP(c_Nat_Ocompow(X2,X1,X3,X3),X4)) = hAPP(c_Nat_Ocompow(X2,X1,X3,X3),hAPP(X1,X4)),
cls_funpow__swap1_0,
[final] ).
cnf(i_0_566,axiom,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB) ),
cls_lifts__IT_0,
[final] ).
cnf(i_0_567,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X4)) ),
cls_subst__preserves__beta2_H_0,
[final] ).
cnf(i_0_568,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X4),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X4)) ),
cls_subst__preserves__beta_H_0,
[final] ).
cnf(i_0_569,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X4)) ),
cls_subst__preserves__beta2_0,
[final] ).
cnf(i_0_570,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),hAPP(hAPP(c_Type_Otype_OFun,X5),X4))) ),
cls_App_0,
[final] ).
cnf(i_0_571,axiom,
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),X4) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X4)),hAPP(hAPP(c_Lambda_Olift,X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
cls_lift__subst__lt_0,
[final] ).
cnf(i_0_572,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),X3)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X4),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X4)) ),
cls_subst__preserves__beta_0,
[final] ).
cnf(i_0_573,axiom,
c_Fun_Ofcomp(c_Fun_Oid(X1),X2,X1,X1,X3) = X2,
cls_id__fcomp_0,
[final] ).
cnf(i_0_574,axiom,
c_Fun_Ocomp(c_Fun_Oid(X1),X2,X1,X1,X3) = X2,
cls_id__o_0,
[final] ).
cnf(i_0_575,axiom,
c_Fun_Ofcomp(X1,c_Fun_Oid(X2),X3,X2,X2) = X1,
cls_fcomp__id_0,
[final] ).
cnf(i_0_576,axiom,
c_Fun_Ocomp(X1,c_Fun_Oid(X2),X2,X3,X2) = X1,
cls_o__id_0,
[final] ).
cnf(i_0_577,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(rw,[status(thm)],[i_0_418,c_0_412]),
[final] ).
cnf(i_0_578,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
cls_rtrancl__beta__App_0,
[final] ).
cnf(i_0_579,axiom,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X2,tc_nat))) ),
cls_nat__diff__split_1,
[final] ).
cnf(i_0_580,axiom,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X2,tc_nat))) ),
cls_nat__diff__split__asm_1,
[final] ).
cnf(i_0_581,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X3),X4)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X2),X3),X4)),
cls_subst__App_0,
[final] ).
cnf(i_0_582,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X1),X2)),hAPP(hAPP(c_Lambda_Olift,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
cls_lift__preserves__beta_H_0,
[final] ).
cnf(i_0_583,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X2),X3)) ),
cls_rtrancl__beta__AppR_0,
[final] ).
cnf(i_0_584,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X1),X3)) ),
cls_rtrancl__beta__AppL_0,
[final] ).
cnf(i_0_585,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(X2,X1) = c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(X1,X1,X1),c_HOL_Oplus__class_Oplus(X1)),c_HOL_Oone__class_Oone(X1)),X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_semiring__1__class_Oof__nat__code_0,
[final] ).
cnf(i_0_586,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))),
cls_beta_0,
[final] ).
cnf(i_0_587,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X1)),X2),X3) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),hAPP(hAPP(c_Lambda_Olift,X2),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
cls_subst__Abs_0,
[final] ).
cnf(i_0_588,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_419,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_589,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
cls_rtranclp__trans_0,
[final] ).
cnf(i_0_590,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) ),
cls_class__semiring_Osemiring__rules_I20_J_0,
[final] ).
cnf(i_0_591,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X4),X2)) ),
cls_subject__reduction_H_0,
[final] ).
cnf(i_0_592,plain,
c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X1),X2),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Type_Otype)),c_Nat_Osize__class_Osize(X2,tc_Type_Otype))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
inference(rw,[status(thm)],[i_0_420,c_0_412]),
[final] ).
cnf(i_0_593,plain,
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X1),X3)),X2)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(rw,[status(thm)],[i_0_421,c_0_412]),
[final] ).
cnf(i_0_594,axiom,
( X1 = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X1,X2,X3)),c_Type_Osko__Type__Xtyping__elims__3__2(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X2),c_Lambda_OdB_OAbs(X3)),X1)) ),
cls_typing__elims_I3_J_0,
[final] ).
cnf(i_0_595,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X1),X2)),hAPP(hAPP(c_Lambda_Olift,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
cls_lift__preserves__beta_0,
[final] ).
cnf(i_0_596,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),X3)) ),
cls_appR_0,
[final] ).
cnf(i_0_597,axiom,
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),hAPP(hAPP(c_Lambda_OdB_OApp,X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X3)) ),
cls_appL_0,
[final] ).
cnf(i_0_598,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X4,X1) = c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X3,hAPP(X2,X4),X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(rw,[status(thm)],[i_0_422,c_0_412]),
[final] ).
cnf(i_0_599,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X5),X4))
| ~ hBOOL(hAPP(hAPP(X1,X3),X5)) ),
cls_converse__rtranclp__into__rtranclp_0,
[final] ).
cnf(i_0_600,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X5)) ),
cls_rtranclp_Ortrancl__into__rtrancl_0,
[final] ).
cnf(i_0_601,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_423,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_602,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X4),X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),X4),X3)) ),
cls_subject__reduction_0,
[final] ).
cnf(i_0_603,axiom,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
cls_COMBC__def_0,
[final] ).
cnf(i_0_604,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat))),X3) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
inference(rw,[status(thm)],[i_0_424,c_0_414]),
[final] ).
cnf(i_0_605,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) ),
cls_class__semiring_Osemiring__rules_I23_J_0,
[final] ).
cnf(i_0_606,plain,
c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(rw,[status(thm)],[i_0_425,c_0_412]),
[final] ).
cnf(i_0_607,plain,
c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(rw,[status(thm)],[i_0_426,c_0_412]),
[final] ).
cnf(i_0_608,plain,
c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(rw,[status(thm)],[i_0_427,c_0_412]),
[final] ).
cnf(i_0_609,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
cls_conjecture_3,
[final] ).
cnf(i_0_610,axiom,
( hBOOL(hAPP(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ hBOOL(hAPP(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat))) ),
cls_nat__diff__split_0,
[final] ).
cnf(i_0_611,plain,
c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X1)),c_Type_Otype_Otype__size(X2))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
inference(rw,[status(thm)],[i_0_428,c_0_412]),
[final] ).
cnf(i_0_612,axiom,
c_Lambda_Oliftn(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X1,X2,X4)),c_Lambda_Oliftn(X1,X3,X4)),
cls_liftn_Osimps_I2_J_0,
[final] ).
cnf(i_0_613,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1) ),
cls_add__less__cancel__right_0,
[final] ).
cnf(i_0_614,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3),X1) ),
cls_add__less__cancel__left_0,
[final] ).
cnf(i_0_615,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),c_HOL_Oone__class_Oone(tc_nat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_429,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_616,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_OdB_OVar(X2)),X3)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
cls_subst__Var__IT_0,
[final] ).
cnf(i_0_617,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)) ),
cls_rtrancl__beta__Abs_0,
[final] ).
cnf(i_0_618,axiom,
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X5) = hAPP(X2,c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X3,X5,tc_nat) ),
cls_shift__lt_0,
[final] ).
cnf(i_0_619,plain,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))),X1) = c_Lambda_Oliftn(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
inference(rw,[status(thm)],[i_0_430,c_0_414]),
[final] ).
cnf(i_0_620,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_431,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_621,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),X5),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__strict__mono_0,
[final] ).
cnf(i_0_622,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(rw,[status(thm)],[i_0_432,c_0_412]),
[final] ).
cnf(i_0_623,axiom,
hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)),X3) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X1),X3)),hAPP(hAPP(c_Lambda_Olift,X2),X3)),
cls_lift_Osimps_I2_J_0,
[final] ).
cnf(i_0_624,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
cls_diff__less__mono2_0,
[final] ).
cnf(i_0_625,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
cls_nat__add__left__cancel__less_0,
[final] ).
cnf(i_0_626,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) ),
cls_comm__monoid__add_Omult__assoc_0,
[final] ).
cnf(i_0_627,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) ),
cls_class__semiring_Osemiring__rules_I21_J_0,
[final] ).
cnf(i_0_628,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) ),
cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,
[final] ).
cnf(i_0_629,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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I25_J_0,
[final] ).
cnf(i_0_630,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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__a_0,
[final] ).
cnf(i_0_631,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X2,c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(rw,[status(thm)],[i_0_433,c_0_414]),
[final] ).
cnf(i_0_632,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_add__less__mono_0,
[final] ).
cnf(i_0_633,plain,
c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,X3) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X1,X2,X3)),X3),
inference(rw,[status(thm)],[i_0_434,c_0_412]),
[final] ).
cnf(i_0_634,plain,
( X1 = X3
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),c_Lambda_Oliftn(X3,X2,c_HOL_Ozero__class_Ozero(tc_nat))),X3) = c_Lambda_OdB_OVar(X1)
| c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
inference(rw,[status(thm)],[i_0_435,c_0_414]),
[final] ).
cnf(i_0_635,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ),
cls_less__diff__conv_0,
[final] ).
cnf(i_0_636,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) = X5
| ~ 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),X5) ),
cls_add__cancel__21_0,
[final] ).
cnf(i_0_637,axiom,
( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
cls_less__diff__conv_1,
[final] ).
cnf(i_0_638,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_436,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_639,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X2)),X3),X2) = X1,
cls_subst__lift_0,
[final] ).
cnf(i_0_640,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),c_HOL_Oone__class_Oone(tc_nat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_437,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_641,axiom,
c_Lambda_Oliftn(X1,c_Lambda_OdB_OAbs(X2),X3) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),
cls_liftn_Osimps_I3_J_0,
[final] ).
cnf(i_0_642,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
cls_nat__add__assoc_0,
[final] ).
cnf(i_0_643,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__neg__neg_0,
[final] ).
cnf(i_0_644,axiom,
( 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)
| ~ 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) ),
cls_add__pos__pos_0,
[final] ).
cnf(i_0_645,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(rw,[status(thm)],[i_0_438,c_0_412]),
[final] ).
cnf(i_0_646,plain,
( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
inference(rw,[status(thm)],[i_0_439,c_0_412]),
[final] ).
cnf(i_0_647,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)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_add__less__cancel__left_1,
[final] ).
cnf(i_0_648,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)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_add__strict__left__mono_0,
[final] ).
cnf(i_0_649,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)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__less__cancel__right_1,
[final] ).
cnf(i_0_650,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)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__strict__right__mono_0,
[final] ).
cnf(i_0_651,axiom,
( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_pos__add__strict_0,
[final] ).
cnf(i_0_652,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(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
cls_add__gr__0_0,
[final] ).
cnf(i_0_653,axiom,
( hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X5) = hAPP(X2,X5)
| ~ c_HOL_Oord__class_Oless(X5,X3,tc_nat) ),
cls_shift__gt_0,
[final] ).
cnf(i_0_654,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat)
| ~ 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(tc_nat),X2,tc_nat) ),
cls_diff__less_0,
[final] ).
cnf(i_0_655,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_440,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_656,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_441,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_657,axiom,
( hAPP(X1,X2) = X3
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),X3)) ),
cls_typing__elims_I1_J_0,
[final] ).
cnf(i_0_658,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_less__iff__diff__less__0_1,
[final] ).
cnf(i_0_659,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ 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) ),
cls_zero__less__double__add__iff__zero__less__single__add_0,
[final] ).
cnf(i_0_660,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ 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) ),
cls_even__less__0__iff_0,
[final] ).
cnf(i_0_661,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ 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) ),
cls_double__add__less__zero__iff__single__less__zero_0,
[final] ).
cnf(i_0_662,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_442,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_663,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_443,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_664,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1) ),
cls_less__eqI_1,
[final] ).
cnf(i_0_665,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_less__eqI_0,
[final] ).
cnf(i_0_666,plain,
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(rw,[status(thm)],[i_0_444,c_0_412]),
[final] ).
cnf(i_0_667,plain,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
inference(rw,[status(thm)],[i_0_445,c_0_412]),
[final] ).
cnf(i_0_668,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
cls_nat__add__left__cancel__less_1,
[final] ).
cnf(i_0_669,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_add__less__mono1_0,
[final] ).
cnf(i_0_670,axiom,
hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X1)),X2) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)))),
cls_lift_Osimps_I3_J_0,
[final] ).
cnf(i_0_671,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) ),
cls_comm__monoid__add_Omult__left__commute_0,
[final] ).
cnf(i_0_672,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) ),
cls_class__semiring_Osemiring__rules_I22_J_0,
[final] ).
cnf(i_0_673,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) ),
cls_add__cancel__21_1,
[final] ).
cnf(i_0_674,axiom,
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
cls_r__into__rtranclp_0,
[final] ).
cnf(i_0_675,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
cls_diff__commute_0,
[final] ).
cnf(i_0_676,plain,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
inference(rw,[status(thm)],[i_0_446,c_0_412]),
[final] ).
cnf(i_0_677,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
cls_subst__Var_0,
[final] ).
cnf(i_0_678,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
cls_subst__gt_0,
[final] ).
cnf(i_0_679,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
cls_zero__less__diff_0,
[final] ).
cnf(i_0_680,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat),
cls_diff__diff__left_0,
[final] ).
cnf(i_0_681,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_447,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_682,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(rw,[status(thm)],[i_0_448,c_0_412]),
[final] ).
cnf(i_0_683,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(rw,[status(thm)],[i_0_449,c_0_412]),
[final] ).
cnf(i_0_684,plain,
( X1 = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(rw,[status(thm)],[i_0_450,c_0_412]),
[final] ).
cnf(i_0_685,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat) ),
inference(rw,[status(thm)],[i_0_451,c_0_412]),
[final] ).
cnf(i_0_686,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
cls_diff__cancel_0,
[final] ).
cnf(i_0_687,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
cls_diff__cancel2_0,
[final] ).
cnf(i_0_688,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = X2
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_452,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_689,axiom,
( c_HOL_Oord__class_Oless(X1,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
cls_less__add__eq__less_0,
[final] ).
cnf(i_0_690,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X2,tc_nat) ),
cls_add__lessD1_0,
[final] ).
cnf(i_0_691,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__add__cancel_0,
[final] ).
cnf(i_0_692,plain,
( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_453,c_0_412]),c_0_412]),c_0_412]),
[final] ).
cnf(i_0_693,plain,
( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_454,c_0_412]),c_0_412]),c_0_412]),
[final] ).
cnf(i_0_694,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
cls_nat__add__left__commute_0,
[final] ).
cnf(i_0_695,axiom,
( 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_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_even__less__0__iff_1,
[final] ).
cnf(i_0_696,axiom,
( 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_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__less__zero__iff__single__less__zero_1,
[final] ).
cnf(i_0_697,axiom,
( 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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__less__double__add__iff__zero__less__single__add_1,
[final] ).
cnf(i_0_698,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_less__iff__diff__less__0_0,
[final] ).
cnf(i_0_699,axiom,
( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,c_HOL_Ozero__class_Ozero(tc_nat),X3,X1) = X3
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_of__nat__aux_Osimps_I1_J_0,
[final] ).
cnf(i_0_700,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(rw,[status(thm)],[i_0_455,c_0_412]),
[final] ).
cnf(i_0_701,axiom,
c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2,X2) = c_Fun_Oid(X2),
cls_funpow_Osimps_I1_J_0,
[final] ).
cnf(i_0_702,plain,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(rw,[status(thm)],[i_0_456,c_0_412]),
[final] ).
cnf(i_0_703,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X1),c_Lambda_OdB_OVar(X2)),hAPP(X1,X2))),
cls_typing_OVar_0,
[final] ).
cnf(i_0_704,axiom,
hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X1),X2),X3),X4),X3) = X4,
cls_shift__eq_0,
[final] ).
cnf(i_0_705,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
cls_zero__less__diff_1,
[final] ).
cnf(i_0_706,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1)),c_Nat_Osemiring__1__class_Oof__nat(X3,X1))
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_of__nat__add_0,
[final] ).
cnf(i_0_707,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_less__imp__diff__less_0,
[final] ).
cnf(i_0_708,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2))))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
cls_app__Var__IT_0,
[final] ).
cnf(i_0_709,axiom,
c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____),v_as____,v_Ts____),
cls_argsT_0,
[final] ).
cnf(i_0_710,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_add__gr__0_1,
[final] ).
cnf(i_0_711,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_add__gr__0_2,
[final] ).
cnf(i_0_712,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_order__less__trans_0,
[final] ).
cnf(i_0_713,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_xt1_I10_J_0,
[final] ).
cnf(i_0_714,plain,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[i_0_457,c_0_412]),
[final] ).
cnf(i_0_715,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)) ),
cls_abs_0,
[final] ).
cnf(i_0_716,axiom,
( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1) ),
cls_of__nat__less__iff_0,
[final] ).
cnf(i_0_717,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_termination__basic__simps_I1_J_0,
[final] ).
cnf(i_0_718,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_trans__less__add1_0,
[final] ).
cnf(i_0_719,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_termination__basic__simps_I2_J_0,
[final] ).
cnf(i_0_720,axiom,
( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_trans__less__add2_0,
[final] ).
cnf(i_0_721,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat),
cls_not__add__less1_0,
[final] ).
cnf(i_0_722,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),
cls_not__add__less2_0,
[final] ).
cnf(i_0_723,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_458,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_724,plain,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_459,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_725,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_460,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_726,plain,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_461,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_727,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_462,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_728,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_463,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_729,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
cls_lift__IT_0,
[final] ).
cnf(i_0_730,axiom,
( c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X3) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1))
| c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
cls_liftn_Osimps_I1_J_1,
[final] ).
cnf(i_0_731,plain,
( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_Nat_Osemiring__1__class_Oof__nat(X2,X1))
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
inference(rw,[status(thm)],[i_0_464,c_0_412]),
[final] ).
cnf(i_0_732,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1)),c_HOL_Oone__class_Oone(X1)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_zero__less__two_0,
[final] ).
cnf(i_0_733,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = X2
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
cls_add__diff__inverse_0,
[final] ).
cnf(i_0_734,axiom,
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_lift_Osimps_I1_J_1,
[final] ).
cnf(i_0_735,plain,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(rw,[status(thm)],[i_0_465,c_0_412]),
[final] ).
cnf(i_0_736,plain,
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(rw,[status(thm)],[i_0_466,c_0_412]),
[final] ).
cnf(i_0_737,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ 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) ),
cls_of__nat__0__less__iff_0,
[final] ).
cnf(i_0_738,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
cls_subst__lt_0,
[final] ).
cnf(i_0_739,axiom,
( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_Nat_Osemiring__1__class_Oof__nat(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
cls_of__nat__less__iff_1,
[final] ).
cnf(i_0_740,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
cls_nat__less__cases_0,
[final] ).
cnf(i_0_741,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
cls_rtranclp_Ortrancl__refl_0,
[final] ).
cnf(i_0_742,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X3)),
cls_Nitpick_Ortranclp__def_1,
[final] ).
cnf(i_0_743,axiom,
( 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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_of__nat__0__less__iff_1,
[final] ).
cnf(i_0_744,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_class__ringb_Oadd__cancel_0,
[final] ).
cnf(i_0_745,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
cls_eq__eqI_1,
[final] ).
cnf(i_0_746,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
cls_eq__eqI_0,
[final] ).
cnf(i_0_747,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_not__less__iff__gr__or__eq_1,
[final] ).
cnf(i_0_748,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_order__less__asym_H_0,
[final] ).
cnf(i_0_749,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_order__less__asym_0,
[final] ).
cnf(i_0_750,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_xt1_I9_J_0,
[final] ).
cnf(i_0_751,axiom,
( X2 = X1
| c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_diffs0__imp__equal_0,
[final] ).
cnf(i_0_752,axiom,
( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Oone__class_Oone(X1)),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_less__add__one_0,
[final] ).
cnf(i_0_753,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
cls_add__right__cancel_0,
[final] ).
cnf(i_0_754,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_add__left__cancel_0,
[final] ).
cnf(i_0_755,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_add__imp__eq_0,
[final] ).
cnf(i_0_756,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X3) = c_Lambda_OdB_OVar(X1)
| X1 = X3
| c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
cls_subst__Var_2,
[final] ).
cnf(i_0_757,plain,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
inference(rw,[status(thm)],[i_0_467,c_0_412]),
[final] ).
cnf(i_0_758,plain,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(rw,[status(thm)],[i_0_468,c_0_412]),
[final] ).
cnf(i_0_759,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_add__diff__cancel_0,
[final] ).
cnf(i_0_760,axiom,
( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2 ),
cls_subst__Var_1,
[final] ).
cnf(i_0_761,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(rw,[status(thm)],[i_0_469,c_0_412]),
[final] ).
cnf(i_0_762,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)),
cls_beta__cases_I1_J_0,
[final] ).
cnf(i_0_763,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_470,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_764,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_471,c_0_412]),c_0_412]),
[final] ).
cnf(i_0_765,plain,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
inference(rw,[status(thm)],[i_0_472,c_0_412]),
[final] ).
cnf(i_0_766,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(rw,[status(thm)],[i_0_473,c_0_412]),
[final] ).
cnf(i_0_767,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(rw,[status(thm)],[i_0_474,c_0_412]),
[final] ).
cnf(i_0_768,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)),
cls_uT_0,
[final] ).
cnf(i_0_769,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
cls_conjecture_2,
[final] ).
cnf(i_0_770,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)),
cls_Var_I4_J_0,
[final] ).
cnf(i_0_771,plain,
c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(rw,[status(thm)],[i_0_475,c_0_412]),
[final] ).
cnf(i_0_772,plain,
c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(rw,[status(thm)],[i_0_476,c_0_412]),
[final] ).
cnf(i_0_773,axiom,
( c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X3) = c_Lambda_OdB_OVar(X2)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
cls_liftn_Osimps_I1_J_0,
[final] ).
cnf(i_0_774,axiom,
( X1 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
cls_nat__add__right__cancel_0,
[final] ).
cnf(i_0_775,axiom,
( X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
cls_nat__add__left__cancel_0,
[final] ).
cnf(i_0_776,axiom,
( X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
cls_natgb_Oadd__cancel_0,
[final] ).
cnf(i_0_777,axiom,
c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_diff__add__0_0,
[final] ).
cnf(i_0_778,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat) = X2,
cls_diff__add__inverse_0,
[final] ).
cnf(i_0_779,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1,
cls_diff__add__inverse2_0,
[final] ).
cnf(i_0_780,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_of__nat__less__0__iff_0,
[final] ).
cnf(i_0_781,axiom,
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X1)),X2) = c_Lambda_OdB_OVar(X1)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_lift_Osimps_I1_J_0,
[final] ).
cnf(i_0_782,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0,
[final] ).
cnf(i_0_783,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__antisym__conv3_0,
[final] ).
cnf(i_0_784,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__less__linear_0,
[final] ).
cnf(i_0_785,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__neqE_0,
[final] ).
cnf(i_0_786,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X3,X2,X1)
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_not__less__iff__gr__or__eq_0,
[final] ).
cnf(i_0_787,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_linorder__neqE__ordered__idom_0,
[final] ).
cnf(i_0_788,axiom,
( X1 = X3
| hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != hAPP(hAPP(c_Type_Otype_OFun,X3),X4) ),
cls_type_Osimps_I2_J_0,
[final] ).
cnf(i_0_789,axiom,
( X1 = X3
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
cls_dB_Osimps_I2_J_0,
[final] ).
cnf(i_0_790,axiom,
( X2 = X4
| hAPP(hAPP(c_Type_Otype_OFun,X1),X2) != hAPP(hAPP(c_Type_Otype_OFun,X3),X4) ),
cls_type_Osimps_I2_J_1,
[final] ).
cnf(i_0_791,axiom,
( X2 = X4
| hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
cls_dB_Osimps_I2_J_1,
[final] ).
cnf(i_0_792,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_not__one__less__zero_0,
[final] ).
cnf(i_0_793,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) ),
cls_comm__monoid__add_Omult__commute_0,
[final] ).
cnf(i_0_794,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) ),
cls_class__semiring_Osemiring__rules_I24_J_0,
[final] ).
cnf(i_0_795,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) ),
cls_class__semiring_Oadd__c_0,
[final] ).
cnf(i_0_796,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
cls_subst__eq_0,
[final] ).
cnf(i_0_797,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
cls_linorder__neqE__nat_0,
[final] ).
cnf(i_0_798,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
cls_nat__neq__iff_0,
[final] ).
cnf(i_0_799,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_class__ringb_Osubr0__iff_0,
[final] ).
cnf(i_0_800,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
cls_class__ringb_Oadd__r0__iff_0,
[final] ).
cnf(i_0_801,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_eq__iff__diff__eq__0_1,
[final] ).
cnf(i_0_802,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_right__minus__eq_0,
[final] ).
cnf(i_0_803,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1),
inference(rw,[status(thm)],[i_0_477,c_0_412]),
[final] ).
cnf(i_0_804,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) != c_HOL_Ozero__class_Ozero(X1) ),
cls_double__eq__0__iff_0,
[final] ).
cnf(i_0_805,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_linorder__neq__iff_1,
[final] ).
cnf(i_0_806,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__irrefl_0,
[final] ).
cnf(i_0_807,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__le_1,
[final] ).
cnf(i_0_808,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_neq0__conv_1,
[final] ).
cnf(i_0_809,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
cls_nat__add__commute_0,
[final] ).
cnf(i_0_810,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_gr__implies__not0_0,
[final] ).
cnf(i_0_811,axiom,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
cls_not__less0_0,
[final] ).
cnf(i_0_812,axiom,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
cls_ATP__Linkup_Ofequal__imp__equal_0,
[final] ).
cnf(i_0_813,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
cls_less__not__refl_0,
[final] ).
cnf(i_0_814,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
cls_nat__less__le_1,
[final] ).
cnf(i_0_815,axiom,
( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1)) ),
cls_Lambda_0,
[final] ).
cnf(i_0_816,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) ),
cls_double__eq__0__iff_1,
[final] ).
cnf(i_0_817,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(rw,[status(thm)],[i_0_478,c_0_412]),
[final] ).
cnf(i_0_818,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(rw,[status(thm)],[i_0_479,c_0_412]),
[final] ).
cnf(i_0_819,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
inference(rw,[status(thm)],[i_0_480,c_0_412]),
[final] ).
cnf(i_0_820,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
inference(rw,[status(thm)],[i_0_481,c_0_412]),
[final] ).
cnf(i_0_821,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_add__is__0_0,
[final] ).
cnf(i_0_822,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_add__is__0_1,
[final] ).
cnf(i_0_823,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != X1,
inference(rw,[status(thm)],[i_0_482,c_0_412]),
[final] ).
cnf(i_0_824,plain,
X1 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
inference(rw,[status(thm)],[i_0_483,c_0_412]),
[final] ).
cnf(i_0_825,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X1 ),
cls_add__eq__self__zero_0,
[final] ).
cnf(i_0_826,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
cls_natgb_Oadd__r0__iff_0,
[final] ).
cnf(i_0_827,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_zero__less__one_0,
[final] ).
cnf(i_0_828,axiom,
( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Oadd__r0__iff_1,
[final] ).
cnf(i_0_829,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Osubr0__iff_1,
[final] ).
cnf(i_0_830,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__1_0,
[final] ).
cnf(i_0_831,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) ),
cls_class__semiring_Osemiring__rules_I5_J_0,
[final] ).
cnf(i_0_832,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) ),
cls_class__semiring_Oadd__0_0,
[final] ).
cnf(i_0_833,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_add__0__left_0,
[final] ).
cnf(i_0_834,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__0__right_0,
[final] ).
cnf(i_0_835,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__1__right_0,
[final] ).
cnf(i_0_836,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) ),
cls_class__semiring_Osemiring__rules_I6_J_0,
[final] ).
cnf(i_0_837,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_monoid__add__class_Oadd__0__right_0,
[final] ).
cnf(i_0_838,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_eq__iff__diff__eq__0_0,
[final] ).
cnf(i_0_839,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_right__minus__eq_1,
[final] ).
cnf(i_0_840,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__self_0,
[final] ).
cnf(i_0_841,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OAbs(X3),
cls_dB_Osimps_I8_J_0,
[final] ).
cnf(i_0_842,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2) != c_Lambda_OdB_OVar(X3),
cls_dB_Osimps_I5_J_0,
[final] ).
cnf(i_0_843,axiom,
c_Lambda_OdB_OAbs(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
cls_dB_Osimps_I9_J_0,
[final] ).
cnf(i_0_844,axiom,
c_Lambda_OdB_OVar(X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),
cls_dB_Osimps_I4_J_0,
[final] ).
cnf(i_0_845,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_gr0I_0,
[final] ).
cnf(i_0_846,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_diff__0__eq__0_0,
[final] ).
cnf(i_0_847,axiom,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
cls_liftn__0_0,
[final] ).
cnf(i_0_848,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_add__is__0_2,
[final] ).
cnf(i_0_849,plain,
c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
inference(rw,[status(thm)],[i_0_484,c_0_412]),
[final] ).
cnf(i_0_850,axiom,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
cls_minus__nat_Odiff__0_0,
[final] ).
cnf(i_0_851,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_diff__self__eq__0_0,
[final] ).
cnf(i_0_852,axiom,
c_fequal(X1,X1,X2),
cls_ATP__Linkup_Oequal__imp__fequal_0,
[final] ).
cnf(i_0_853,axiom,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X1,X2),X2) = c_Transitive__Closure_Ortranclp(X1,X2),
cls_rtranclp__idemp_0,
[final] ).
cnf(i_0_854,axiom,
( X2 = X3
| ~ class_Nat_Osemiring__char__0(X1)
| c_Nat_Osemiring__1__class_Oof__nat(X2,X1) != c_Nat_Osemiring__1__class_Oof__nat(X3,X1) ),
cls_of__nat__eq__iff_0,
[final] ).
cnf(i_0_855,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) = X1,
cls_plus__nat_Oadd__0_0,
[final] ).
cnf(i_0_856,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
cls_Nat_Oadd__0__right_0,
[final] ).
cnf(i_0_857,axiom,
X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
cls_natgb_Oadd__r0__iff_1,
[final] ).
cnf(i_0_858,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1))),
cls_Var__IT_0,
[final] ).
cnf(i_0_859,axiom,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
clsarity_fun__Orderings_Opreorder,
[final] ).
cnf(i_0_860,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
clsarity_fun__Orderings_Oorder,
[final] ).
cnf(i_0_861,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Osemiring__1(X1) ),
cls_of__nat__1_0,
[final] ).
cnf(i_0_862,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) ),
cls_of__nat__0_0,
[final] ).
cnf(i_0_863,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
cls_conjecture_1,
[final] ).
cnf(i_0_864,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
cls_Var_I3_J_0,
[final] ).
cnf(i_0_865,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
cls_uIT_0,
[final] ).
cnf(i_0_866,axiom,
hAPP(c_Fun_Oid(X1),X2) = X2,
cls_id__apply_0,
[final] ).
cnf(i_0_867,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
cls_zero__neq__one_0,
[final] ).
cnf(i_0_868,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_one__neq__zero_0,
[final] ).
cnf(i_0_869,axiom,
hAPP(c_Fun_Oid(t_a),v_x) = v_x,
cls_id__def_0,
[final] ).
cnf(i_0_870,axiom,
( X1 = X2
| c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
cls_dB_Osimps_I3_J_0,
[final] ).
cnf(i_0_871,axiom,
( X1 = X2
| c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
cls_dB_Osimps_I1_J_0,
[final] ).
cnf(i_0_872,axiom,
c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OVar(X2),
cls_dB_Osimps_I7_J_0,
[final] ).
cnf(i_0_873,axiom,
c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
cls_dB_Osimps_I6_J_0,
[final] ).
cnf(i_0_874,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder,
[final] ).
cnf(i_0_875,axiom,
class_Orderings_Opreorder(tc_bool),
clsarity_bool__Orderings_Opreorder,
[final] ).
cnf(i_0_876,axiom,
class_Orderings_Opreorder(tc_nat),
clsarity_nat__Orderings_Opreorder,
[final] ).
cnf(i_0_877,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder,
[final] ).
cnf(i_0_878,axiom,
class_Orderings_Oorder(tc_nat),
clsarity_nat__Orderings_Oorder,
[final] ).
cnf(i_0_879,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_880,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_881,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
clsarity_nat__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_882,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_883,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Osemigroup__add,
[final] ).
cnf(i_0_884,axiom,
class_Nat_Osemiring__char__0(tc_nat),
clsarity_nat__Nat_Osemiring__char__0,
[final] ).
cnf(i_0_885,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_886,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,
[final] ).
cnf(i_0_887,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
[final] ).
cnf(i_0_888,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
clsarity_nat__Ring__and__Field_Oordered__semidom,
[final] ).
cnf(i_0_889,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,
[final] ).
cnf(i_0_890,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
clsarity_nat__Ring__and__Field_Ozero__neq__one,
[final] ).
cnf(i_0_891,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
clsarity_nat__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_892,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring__1,
[final] ).
cnf(i_0_893,axiom,
v_n____ = v_i____,
cls_True_0,
[final] ).
cnf(i_0_894,axiom,
X1 = X1 ).
cnf(i_0_895,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_896,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_897,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_898,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_899,axiom,
( X1 != X2
| c_List_Ofoldl(X1,X3,X4,X5,X6) = c_List_Ofoldl(X2,X3,X4,X5,X6) ) ).
cnf(i_0_900,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X1,X4,X5,X6) = c_List_Ofoldl(X3,X2,X4,X5,X6) ) ).
cnf(i_0_901,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X1,X5,X6) = c_List_Ofoldl(X3,X4,X2,X5,X6) ) ).
cnf(i_0_902,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X5,X1,X6) = c_List_Ofoldl(X3,X4,X5,X2,X6) ) ).
cnf(i_0_903,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X5,X6,X1) = c_List_Ofoldl(X3,X4,X5,X6,X2) ) ).
cnf(i_0_904,axiom,
( X1 != X2
| c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).
cnf(i_0_905,axiom,
( X1 != X2
| c_List_Omap(X1,X3,X4,X5) = c_List_Omap(X2,X3,X4,X5) ) ).
cnf(i_0_906,axiom,
( X1 != X2
| c_List_Omap(X3,X1,X4,X5) = c_List_Omap(X3,X2,X4,X5) ) ).
cnf(i_0_907,axiom,
( X1 != X2
| c_List_Omap(X3,X4,X1,X5) = c_List_Omap(X3,X4,X2,X5) ) ).
cnf(i_0_908,axiom,
( X1 != X2
| c_List_Omap(X3,X4,X5,X1) = c_List_Omap(X3,X4,X5,X2) ) ).
cnf(i_0_909,axiom,
( X1 != X2
| c_Transitive__Closure_Ortranclp(X1,X3) = c_Transitive__Closure_Ortranclp(X2,X3) ) ).
cnf(i_0_910,axiom,
( X1 != X2
| c_Transitive__Closure_Ortranclp(X3,X1) = c_Transitive__Closure_Ortranclp(X3,X2) ) ).
cnf(i_0_911,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_912,axiom,
( X1 != X2
| c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).
cnf(i_0_913,axiom,
( X1 != X2
| c_Fun_Ofcomp(X1,X3,X4,X5,X6) = c_Fun_Ofcomp(X2,X3,X4,X5,X6) ) ).
cnf(i_0_914,axiom,
( X1 != X2
| c_Fun_Ofcomp(X3,X1,X4,X5,X6) = c_Fun_Ofcomp(X3,X2,X4,X5,X6) ) ).
cnf(i_0_915,axiom,
( X1 != X2
| c_Fun_Ofcomp(X3,X4,X1,X5,X6) = c_Fun_Ofcomp(X3,X4,X2,X5,X6) ) ).
cnf(i_0_916,axiom,
( X1 != X2
| c_Fun_Ofcomp(X3,X4,X5,X1,X6) = c_Fun_Ofcomp(X3,X4,X5,X2,X6) ) ).
cnf(i_0_917,axiom,
( X1 != X2
| c_Fun_Ofcomp(X3,X4,X5,X6,X1) = c_Fun_Ofcomp(X3,X4,X5,X6,X2) ) ).
cnf(i_0_918,axiom,
( X1 != X2
| c_Fun_Ocomp(X1,X3,X4,X5,X6) = c_Fun_Ocomp(X2,X3,X4,X5,X6) ) ).
cnf(i_0_919,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X1,X4,X5,X6) = c_Fun_Ocomp(X3,X2,X4,X5,X6) ) ).
cnf(i_0_920,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X1,X5,X6) = c_Fun_Ocomp(X3,X4,X2,X5,X6) ) ).
cnf(i_0_921,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X5,X1,X6) = c_Fun_Ocomp(X3,X4,X5,X2,X6) ) ).
cnf(i_0_922,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X5,X6,X1) = c_Fun_Ocomp(X3,X4,X5,X6,X2) ) ).
cnf(i_0_923,axiom,
( X1 != X2
| c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).
cnf(i_0_924,axiom,
( X1 != X2
| c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).
cnf(i_0_925,axiom,
( X1 != X2
| c_Nat_Ocompow(X1,X3,X4,X5) = c_Nat_Ocompow(X2,X3,X4,X5) ) ).
cnf(i_0_926,axiom,
( X1 != X2
| c_Nat_Ocompow(X3,X1,X4,X5) = c_Nat_Ocompow(X3,X2,X4,X5) ) ).
cnf(i_0_927,axiom,
( X1 != X2
| c_Nat_Ocompow(X3,X4,X1,X5) = c_Nat_Ocompow(X3,X4,X2,X5) ) ).
cnf(i_0_928,axiom,
( X1 != X2
| c_Nat_Ocompow(X3,X4,X5,X1) = c_Nat_Ocompow(X3,X4,X5,X2) ) ).
cnf(i_0_929,axiom,
( X1 != X2
| c_Lambda_Oliftn(X1,X3,X4) = c_Lambda_Oliftn(X2,X3,X4) ) ).
cnf(i_0_930,axiom,
( X1 != X2
| c_Lambda_Oliftn(X3,X1,X4) = c_Lambda_Oliftn(X3,X2,X4) ) ).
cnf(i_0_931,axiom,
( X1 != X2
| c_Lambda_Oliftn(X3,X4,X1) = c_Lambda_Oliftn(X3,X4,X2) ) ).
cnf(i_0_932,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_933,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_934,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_935,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).
cnf(i_0_936,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).
cnf(i_0_937,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X3,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X3,X4,X5) ) ).
cnf(i_0_938,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X1,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X2,X4,X5) ) ).
cnf(i_0_939,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X1,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X2,X5) ) ).
cnf(i_0_940,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X1) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X2) ) ).
cnf(i_0_941,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_942,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_943,axiom,
( X1 != X2
| c_Type_Otype_Otype__size(X1) = c_Type_Otype_Otype__size(X2) ) ).
cnf(i_0_944,axiom,
( X1 != X2
| c_List_Ofoldr(X1,X3,X4,X5,X6) = c_List_Ofoldr(X2,X3,X4,X5,X6) ) ).
cnf(i_0_945,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X1,X4,X5,X6) = c_List_Ofoldr(X3,X2,X4,X5,X6) ) ).
cnf(i_0_946,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X4,X1,X5,X6) = c_List_Ofoldr(X3,X4,X2,X5,X6) ) ).
cnf(i_0_947,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X4,X5,X1,X6) = c_List_Ofoldr(X3,X4,X5,X2,X6) ) ).
cnf(i_0_948,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X4,X5,X6,X1) = c_List_Ofoldr(X3,X4,X5,X6,X2) ) ).
cnf(i_0_949,axiom,
( X1 != X2
| ~ c_List_Olistsp(X1,X3,X4)
| c_List_Olistsp(X2,X3,X4) ) ).
cnf(i_0_950,axiom,
( X1 != X2
| ~ c_List_Olistsp(X3,X1,X4)
| c_List_Olistsp(X3,X2,X4) ) ).
cnf(i_0_951,axiom,
( X1 != X2
| ~ c_List_Olistsp(X3,X4,X1)
| c_List_Olistsp(X3,X4,X2) ) ).
cnf(i_0_952,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_953,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_954,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_955,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_956,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_957,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).
cnf(i_0_958,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| class_Ring__and__Field_Oordered__semidom(X2) ) ).
cnf(i_0_959,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_960,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_961,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_962,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_963,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_964,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_965,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_966,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_967,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_968,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_969,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_970,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_971,axiom,
( X1 != X2
| ~ c_fequal(X1,X3,X4)
| c_fequal(X2,X3,X4) ) ).
cnf(i_0_972,axiom,
( X1 != X2
| ~ c_fequal(X3,X1,X4)
| c_fequal(X3,X2,X4) ) ).
cnf(i_0_973,axiom,
( X1 != X2
| ~ c_fequal(X3,X4,X1)
| c_fequal(X3,X4,X2) ) ).
cnf(i_0_974,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_975,axiom,
( X1 != X2
| ~ c_Type_Otypings(X1,X3,X4)
| c_Type_Otypings(X2,X3,X4) ) ).
cnf(i_0_976,axiom,
( X1 != X2
| ~ c_Type_Otypings(X3,X1,X4)
| c_Type_Otypings(X3,X2,X4) ) ).
cnf(i_0_977,axiom,
( X1 != X2
| ~ c_Type_Otypings(X3,X4,X1)
| c_Type_Otypings(X3,X4,X2) ) ).
cnf(i_0_978,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| class_Ring__and__Field_Ozero__neq__one(X2) ) ).
cnf(i_0_979,axiom,
( X1 != X2
| ~ c_ListOrder_Ostep1(X1,X3,X4,X5)
| c_ListOrder_Ostep1(X2,X3,X4,X5) ) ).
cnf(i_0_980,axiom,
( X1 != X2
| ~ c_ListOrder_Ostep1(X3,X1,X4,X5)
| c_ListOrder_Ostep1(X3,X2,X4,X5) ) ).
cnf(i_0_981,axiom,
( X1 != X2
| ~ c_ListOrder_Ostep1(X3,X4,X1,X5)
| c_ListOrder_Ostep1(X3,X4,X2,X5) ) ).
cnf(i_0_982,axiom,
( X1 != X2
| ~ c_ListOrder_Ostep1(X3,X4,X5,X1)
| c_ListOrder_Ostep1(X3,X4,X5,X2) ) ).
cnf(i_0_983,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_984,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_985,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_986,axiom,
( X1 != X2
| ~ class_OrderedGroup_Osemigroup__add(X1)
| class_OrderedGroup_Osemigroup__add(X2) ) ).
cnf(i_0_987,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_988,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_989,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__1(X1)
| class_Ring__and__Field_Osemiring__1(X2) ) ).
cnf(i_0_894_001,axiom,
X1 = X1 ).
cnf(i_0_895_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_896_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_897_004,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_898_005,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_899_006,axiom,
( X1 != X2
| c_List_Ofoldl(X1,X3,X4,X5,X6) = c_List_Ofoldl(X2,X3,X4,X5,X6) ) ).
cnf(i_0_900_007,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X1,X4,X5,X6) = c_List_Ofoldl(X3,X2,X4,X5,X6) ) ).
cnf(i_0_901_008,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X1,X5,X6) = c_List_Ofoldl(X3,X4,X2,X5,X6) ) ).
cnf(i_0_902_009,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X5,X1,X6) = c_List_Ofoldl(X3,X4,X5,X2,X6) ) ).
cnf(i_0_903_010,axiom,
( X1 != X2
| c_List_Ofoldl(X3,X4,X5,X6,X1) = c_List_Ofoldl(X3,X4,X5,X6,X2) ) ).
cnf(i_0_904_011,axiom,
( X1 != X2
| c_Lambda_OdB_OVar(X1) = c_Lambda_OdB_OVar(X2) ) ).
cnf(i_0_905_012,axiom,
( X1 != X2
| c_List_Omap(X1,X3,X4,X5) = c_List_Omap(X2,X3,X4,X5) ) ).
cnf(i_0_906_013,axiom,
( X1 != X2
| c_List_Omap(X3,X1,X4,X5) = c_List_Omap(X3,X2,X4,X5) ) ).
cnf(i_0_907_014,axiom,
( X1 != X2
| c_List_Omap(X3,X4,X1,X5) = c_List_Omap(X3,X4,X2,X5) ) ).
cnf(i_0_908_015,axiom,
( X1 != X2
| c_List_Omap(X3,X4,X5,X1) = c_List_Omap(X3,X4,X5,X2) ) ).
cnf(i_0_909_016,axiom,
( X1 != X2
| c_Transitive__Closure_Ortranclp(X1,X3) = c_Transitive__Closure_Ortranclp(X2,X3) ) ).
cnf(i_0_910_017,axiom,
( X1 != X2
| c_Transitive__Closure_Ortranclp(X3,X1) = c_Transitive__Closure_Ortranclp(X3,X2) ) ).
cnf(i_0_911_018,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_912_019,axiom,
( X1 != X2
| c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(X2) ) ).
cnf(i_0_913_020,axiom,
( X1 != X2
| c_Fun_Ofcomp(X1,X3,X4,X5,X6) = c_Fun_Ofcomp(X2,X3,X4,X5,X6) ) ).
cnf(i_0_914_021,axiom,
( X1 != X2
| c_Fun_Ofcomp(X3,X1,X4,X5,X6) = c_Fun_Ofcomp(X3,X2,X4,X5,X6) ) ).
cnf(i_0_915_022,axiom,
( X1 != X2
| c_Fun_Ofcomp(X3,X4,X1,X5,X6) = c_Fun_Ofcomp(X3,X4,X2,X5,X6) ) ).
cnf(i_0_916_023,axiom,
( X1 != X2
| c_Fun_Ofcomp(X3,X4,X5,X1,X6) = c_Fun_Ofcomp(X3,X4,X5,X2,X6) ) ).
cnf(i_0_917_024,axiom,
( X1 != X2
| c_Fun_Ofcomp(X3,X4,X5,X6,X1) = c_Fun_Ofcomp(X3,X4,X5,X6,X2) ) ).
cnf(i_0_918_025,axiom,
( X1 != X2
| c_Fun_Ocomp(X1,X3,X4,X5,X6) = c_Fun_Ocomp(X2,X3,X4,X5,X6) ) ).
cnf(i_0_919_026,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X1,X4,X5,X6) = c_Fun_Ocomp(X3,X2,X4,X5,X6) ) ).
cnf(i_0_920_027,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X1,X5,X6) = c_Fun_Ocomp(X3,X4,X2,X5,X6) ) ).
cnf(i_0_921_028,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X5,X1,X6) = c_Fun_Ocomp(X3,X4,X5,X2,X6) ) ).
cnf(i_0_922_029,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X5,X6,X1) = c_Fun_Ocomp(X3,X4,X5,X6,X2) ) ).
cnf(i_0_923_030,axiom,
( X1 != X2
| c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).
cnf(i_0_924_031,axiom,
( X1 != X2
| c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).
cnf(i_0_925_032,axiom,
( X1 != X2
| c_Nat_Ocompow(X1,X3,X4,X5) = c_Nat_Ocompow(X2,X3,X4,X5) ) ).
cnf(i_0_926_033,axiom,
( X1 != X2
| c_Nat_Ocompow(X3,X1,X4,X5) = c_Nat_Ocompow(X3,X2,X4,X5) ) ).
cnf(i_0_927_034,axiom,
( X1 != X2
| c_Nat_Ocompow(X3,X4,X1,X5) = c_Nat_Ocompow(X3,X4,X2,X5) ) ).
cnf(i_0_928_035,axiom,
( X1 != X2
| c_Nat_Ocompow(X3,X4,X5,X1) = c_Nat_Ocompow(X3,X4,X5,X2) ) ).
cnf(i_0_929_036,axiom,
( X1 != X2
| c_Lambda_Oliftn(X1,X3,X4) = c_Lambda_Oliftn(X2,X3,X4) ) ).
cnf(i_0_930_037,axiom,
( X1 != X2
| c_Lambda_Oliftn(X3,X1,X4) = c_Lambda_Oliftn(X3,X2,X4) ) ).
cnf(i_0_931_038,axiom,
( X1 != X2
| c_Lambda_Oliftn(X3,X4,X1) = c_Lambda_Oliftn(X3,X4,X2) ) ).
cnf(i_0_932_039,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_933_040,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_934_041,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_935_042,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ).
cnf(i_0_936_043,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat(X3,X1) = c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ).
cnf(i_0_937_044,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X3,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X3,X4,X5) ) ).
cnf(i_0_938_045,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X1,X4,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X2,X4,X5) ) ).
cnf(i_0_939_046,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X1,X5) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X2,X5) ) ).
cnf(i_0_940_047,axiom,
( X1 != X2
| c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X1) = c_Nat_Osemiring__1__class_Oof__nat__aux(X3,X4,X5,X2) ) ).
cnf(i_0_941_048,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_942_049,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_943_050,axiom,
( X1 != X2
| c_Type_Otype_Otype__size(X1) = c_Type_Otype_Otype__size(X2) ) ).
cnf(i_0_944_051,axiom,
( X1 != X2
| c_List_Ofoldr(X1,X3,X4,X5,X6) = c_List_Ofoldr(X2,X3,X4,X5,X6) ) ).
cnf(i_0_945_052,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X1,X4,X5,X6) = c_List_Ofoldr(X3,X2,X4,X5,X6) ) ).
cnf(i_0_946_053,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X4,X1,X5,X6) = c_List_Ofoldr(X3,X4,X2,X5,X6) ) ).
cnf(i_0_947_054,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X4,X5,X1,X6) = c_List_Ofoldr(X3,X4,X5,X2,X6) ) ).
cnf(i_0_948_055,axiom,
( X1 != X2
| c_List_Ofoldr(X3,X4,X5,X6,X1) = c_List_Ofoldr(X3,X4,X5,X6,X2) ) ).
cnf(i_0_949_056,axiom,
( X1 != X2
| ~ c_List_Olistsp(X1,X3,X4)
| c_List_Olistsp(X2,X3,X4) ) ).
cnf(i_0_950_057,axiom,
( X1 != X2
| ~ c_List_Olistsp(X3,X1,X4)
| c_List_Olistsp(X3,X2,X4) ) ).
cnf(i_0_951_058,axiom,
( X1 != X2
| ~ c_List_Olistsp(X3,X4,X1)
| c_List_Olistsp(X3,X4,X2) ) ).
cnf(i_0_952_059,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_953_060,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_954_061,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_955_062,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_956_063,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_957_064,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).
cnf(i_0_958_065,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| class_Ring__and__Field_Oordered__semidom(X2) ) ).
cnf(i_0_959_066,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_960_067,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_961_068,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_962_069,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_963_070,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_964_071,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_965_072,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_966_073,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_967_074,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_968_075,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_969_076,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_970_077,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_971_078,axiom,
( X1 != X2
| ~ c_fequal(X1,X3,X4)
| c_fequal(X2,X3,X4) ) ).
cnf(i_0_972_079,axiom,
( X1 != X2
| ~ c_fequal(X3,X1,X4)
| c_fequal(X3,X2,X4) ) ).
cnf(i_0_973_080,axiom,
( X1 != X2
| ~ c_fequal(X3,X4,X1)
| c_fequal(X3,X4,X2) ) ).
cnf(i_0_974_081,axiom,
( X1 != X2
| ~ class_Nat_Osemiring__char__0(X1)
| class_Nat_Osemiring__char__0(X2) ) ).
cnf(i_0_975_082,axiom,
( X1 != X2
| ~ c_Type_Otypings(X1,X3,X4)
| c_Type_Otypings(X2,X3,X4) ) ).
cnf(i_0_976_083,axiom,
( X1 != X2
| ~ c_Type_Otypings(X3,X1,X4)
| c_Type_Otypings(X3,X2,X4) ) ).
cnf(i_0_977_084,axiom,
( X1 != X2
| ~ c_Type_Otypings(X3,X4,X1)
| c_Type_Otypings(X3,X4,X2) ) ).
cnf(i_0_978_085,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| class_Ring__and__Field_Ozero__neq__one(X2) ) ).
cnf(i_0_979_086,axiom,
( X1 != X2
| ~ c_ListOrder_Ostep1(X1,X3,X4,X5)
| c_ListOrder_Ostep1(X2,X3,X4,X5) ) ).
cnf(i_0_980_087,axiom,
( X1 != X2
| ~ c_ListOrder_Ostep1(X3,X1,X4,X5)
| c_ListOrder_Ostep1(X3,X2,X4,X5) ) ).
cnf(i_0_981_088,axiom,
( X1 != X2
| ~ c_ListOrder_Ostep1(X3,X4,X1,X5)
| c_ListOrder_Ostep1(X3,X4,X2,X5) ) ).
cnf(i_0_982_089,axiom,
( X1 != X2
| ~ c_ListOrder_Ostep1(X3,X4,X5,X1)
| c_ListOrder_Ostep1(X3,X4,X5,X2) ) ).
cnf(i_0_983_090,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_984_091,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_985_092,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_986_093,axiom,
( X1 != X2
| ~ class_OrderedGroup_Osemigroup__add(X1)
| class_OrderedGroup_Osemigroup__add(X2) ) ).
cnf(i_0_987_094,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_988_095,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_989_096,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__1(X1)
| class_Ring__and__Field_Osemiring__1(X2) ) ).
cnf(i_0_990,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X1,X2,X7,X4,X8),X6),
inference(equality_inference,[],[515]) ).
cnf(i_0_991,plain,
hAPP(X1,hAPP(X2,X3)) = hAPP(X1,hAPP(X2,X3)),
inference(equality_inference,[],[520]) ).
cnf(i_0_992,plain,
hAPP(c_Fun_Oid(X1),hAPP(X2,X3)) = hAPP(X2,X3),
inference(equality_inference,[],[521]) ).
cnf(i_0_993,plain,
X1 = X1,
inference(equality_inference,[],[522]) ).
cnf(i_0_994,plain,
X1 = X1,
inference(equality_inference,[],[523]) ).
cnf(i_0_995,plain,
X1 = X1,
inference(equality_inference,[],[524]) ).
cnf(i_0_996,plain,
X1 = X1,
inference(equality_inference,[],[525]) ).
cnf(i_0_997,plain,
X1 = X1,
inference(equality_inference,[],[528]) ).
cnf(i_0_998,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
inference(equality_inference,[],[636]) ).
cnf(i_0_999,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(equality_inference,[],[692]) ).
cnf(i_0_1000,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(equality_inference,[],[693]) ).
cnf(i_0_1001,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(equality_inference,[],[723]) ).
cnf(i_0_1002,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(equality_inference,[],[724]) ).
cnf(i_0_1003,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(equality_inference,[],[725]) ).
cnf(i_0_1004,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(equality_inference,[],[726]) ).
cnf(i_0_1005,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[744]) ).
cnf(i_0_1006,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[745]) ).
cnf(i_0_1007,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[746]) ).
cnf(i_0_1008,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[753]) ).
cnf(i_0_1009,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[754]) ).
cnf(i_0_1010,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[755]) ).
cnf(i_0_1011,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(equality_inference,[],[757]) ).
cnf(i_0_1012,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(equality_inference,[],[758]) ).
cnf(i_0_1013,plain,
X1 = X1,
inference(equality_inference,[],[774]) ).
cnf(i_0_1014,plain,
X1 = X1,
inference(equality_inference,[],[776]) ).
cnf(i_0_1015,plain,
X1 = X1,
inference(equality_inference,[],[788]) ).
cnf(i_0_1016,plain,
X1 = X1,
inference(equality_inference,[],[789]) ).
cnf(i_0_1017,plain,
X1 = X1,
inference(equality_inference,[],[790]) ).
cnf(i_0_1018,plain,
X1 = X1,
inference(equality_inference,[],[791]) ).
cnf(i_0_1019,plain,
( X1 = X1
| ~ class_Nat_Osemiring__char__0(X2) ),
inference(equality_inference,[],[854]) ).
cnf(i_0_1020,plain,
X1 = X1,
inference(equality_inference,[],[870]) ).
cnf(i_0_1021,plain,
X1 = X1,
inference(equality_inference,[],[871]) ).
cnf(i_0_1022,plain,
$false,
inference(scs_inference,[],[i_0_609,i_0_769,i_0_863,i_0_564,i_0_534]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL806-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n017.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 23:08:27 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.71/1.67 % Version : CSE_E---1.7
% 0.71/1.67 % Problem : theBenchmark.p
% 0.71/1.67 % SZS status Unsatisfiable for theBenchmark.p
% 0.71/1.67 % SZS output start CNFRefutation
% See solution above
% 0.75/1.73 % Total time : 1.326s
%------------------------------------------------------------------------------