%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL821-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.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 04:45:09 PM UTC 2026
% Result : Unsatisfiable 1.00s 1.61s
% Output : CNFRefutation 2.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL821-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n031.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 23:12:08 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.00/1.61 % Version : CSE_E---1.7
% 1.00/1.61 % Problem : theBenchmark.p
% 1.00/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 1.00/1.61 % SZS output start CNFRefutation
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_subst__subst_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Suc__eq__plus1_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_substn_Osimps_I2_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_substn__subst__n_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_substn_Osimps_I3_J_0)).
% 1.00/1.61 cnf(cls_shift__commute_0, axiom, (c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4)=c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),c_Suc(X2),X3,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_shift__commute_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__eq__if_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Suc__pred_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_lift__lift_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_of__nat__aux_Osimps_I2_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Suc__diff__diff_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_substn_Osimps_I1_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__add__Suc1_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__iff__Suc__add_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__add__Suc2_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__Suc_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_substn_Osimps_I1_J_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Suc__less__eq_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__Suc__less_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_substn__subst__0_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_liftn__lift_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_substn_Osimps_I1_J_2)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__Suc__shift_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__Suc__right_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Suc__diff__1_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Suc__pred_H_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Suc__mono_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__Suc__eq__0__disj_3)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__is__1_4)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_one__is__add_4)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_not__less__eq_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__trans__Suc_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__Suc__eq__diff__pred_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__Suc__Suc_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__SucE_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_not__less__less__Suc__eq_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__antisym_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Suc__lessD_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Suc__lessI_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_one__is__add_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__is__1_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__Suc0_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__less__Suc_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__SucI_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_one__is__add_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_one__is__add_3)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__is__1_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__is__1_3)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__is__1_5)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_one__is__add_5)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_of__nat__Suc_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_not__less__less__Suc__eq_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_not__less__eq_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_one__is__add_2)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__is__1_2)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__Suc0_1)).
% 1.00/1.61 cnf(cls_Suc__inject_0, axiom, (X1=X2|c_Suc(X1)!=c_Suc(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Suc__inject_0)).
% 1.00/1.61 cnf(cls_nat_Oinject_0, axiom, (X1=X2|c_Suc(X1)!=c_Suc(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_nat_Oinject_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__Suc__1_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_gr0__conv__Suc_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_zero__less__Suc_0)).
% 1.00/1.61 cnf(cls_lessI_0, axiom, (c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_lessI_0)).
% 1.00/1.61 cnf(cls_less__Suc__eq_2, axiom, (c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_less__Suc__eq_2)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Suc__eq__plus1__left_0)).
% 1.00/1.61 cnf(cls_nat_Osimps_I3_J_0, axiom, (c_Suc(X1)!=c_HOL_Ozero__class_Ozero(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_nat_Osimps_I3_J_0)).
% 1.00/1.61 cnf(cls_Suc__neq__Zero_0, axiom, (c_Suc(X1)!=c_HOL_Ozero__class_Ozero(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Suc__neq__Zero_0)).
% 1.00/1.61 cnf(cls_nat_Osimps_I2_J_0, axiom, (c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_nat_Osimps_I2_J_0)).
% 1.00/1.61 cnf(cls_Zero__neq__Suc_0, axiom, (c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Zero__neq__Suc_0)).
% 1.00/1.61 cnf(cls_Suc__n__not__n_0, axiom, (c_Suc(X1)!=X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Suc__n__not__n_0)).
% 1.00/1.61 cnf(cls_n__not__Suc__n_0, axiom, (X1!=c_Suc(X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_n__not__Suc__n_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_One__nat__def_0)).
% 1.00/1.61 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(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_subst__map_0)).
% 1.00/1.61 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)|~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)|~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/sandbox2/benchmark/theBenchmark.p', cls_var__app__types_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_head__Var__reduction_1)).
% 1.00/1.61 cnf(cls_substs__lemma_0, axiom, (c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)|~c_Type_Otypings(c_Type_Oshift(X1,X3,X6,tc_Type_Otype),X4,X5)|~c_Type_Otyping(X1,X2,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_substs__lemma_0)).
% 1.00/1.61 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))|~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)|~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/sandbox2/benchmark/theBenchmark.p', cls_var__app__types_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_head__Var__reduction_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_apps__preserves__betas_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_apps__preserves__beta_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Beta_0)).
% 1.00/1.61 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(c_COMBC(c_Lambda_Olift,X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_lift__map_0)).
% 1.00/1.61 cnf(cls_var__app__type__eq_0, axiom, (X1=X2|~c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X2)|~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/sandbox2/benchmark/theBenchmark.p', cls_var__app__type__eq_0)).
% 1.00/1.61 cnf(cls_var__app__typesE_0, axiom, (c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))|~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/sandbox2/benchmark/theBenchmark.p', cls_var__app__typesE_0)).
% 1.00/1.61 cnf(cls_list__app__typeD_0, axiom, (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))|~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_list__app__typeD_0)).
% 1.00/1.61 cnf(cls_list__app__typeE_0, axiom, (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))|~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X4,tc_Lambda_OdB,tc_Lambda_OdB),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_list__app__typeE_0)).
% 1.00/1.61 cnf(cls_list__app__typeI_0, axiom, (c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)|~c_Type_Otypings(X1,X3,X5)|~c_Type_Otyping(X1,X2,c_List_Ofoldr(c_Type_Otype_OFun,X5,X4,tc_Type_Otype,tc_Type_Otype))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_list__app__typeI_0)).
% 1.00/1.61 cnf(cls_lift__types_0, axiom, (c_Type_Otypings(c_Type_Oshift(X1,X2,X3,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X2,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)|~c_Type_Otypings(X1,X4,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_lift__types_0)).
% 1.00/1.61 cnf(cls_lifts__IT_0, axiom, (c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)|~c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_lifts__IT_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_IT_OVar_0)).
% 1.00/1.61 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))|~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/sandbox2/benchmark/theBenchmark.p', cls_var__app__typesE_1)).
% 1.00/1.61 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))|~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_list__app__typeD_1)).
% 1.00/1.61 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))|~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X4,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_list__app__typeE_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Var__apps__eq__Var__apps__conv_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Abs__apps__eq__Abs__apps__conv_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Var__apps__eq__Var__apps__conv_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Abs__apps__eq__Abs__apps__conv_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_foldl__assoc_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Var__apps__neq__Abs__apps_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_apps__eq__tail__conv_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_foldl__absorb0_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_foldl__foldr1__lemma_0)).
% 1.00/1.61 cnf(cls_CHAINED_0, axiom, (c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_CHAINED_0)).
% 1.00/1.61 cnf(cls_nT_0, axiom, (c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_nT_0)).
% 1.00/1.61 cnf(cls_Var_I2_J_0, axiom, (c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Var_I2_J_0)).
% 1.00/1.61 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(c_COMBC(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1),X1,X1,X1),X2,c_HOL_Ozero__class_Ozero(X1),X1)|~class_Ring__and__Field_Osemiring__1(X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_semiring__1__class_Oof__nat__code_0)).
% 1.00/1.61 cnf(cls_COMBC__def_0, axiom, (hAPP(c_COMBC(X1,X2,X3,X4,X5),X6)=hAPP(hAPP(X1,X6),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_COMBC__def_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_foldl__foldr1_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_foldr__conv__foldl_0)).
% 1.00/1.61 cnf(cls_typing__elims_I2_J_0, axiom, (c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X2,X4)),X3))|~c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_typing__elims_I2_J_0)).
% 1.00/1.61 cnf(cls_App__eq__foldl__conv_0, axiom, (hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)=X3|hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)!=c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_App__eq__foldl__conv_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Abs__App__neq__Var__apps_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Var__eq__apps__conv_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Abs__eq__apps__conv_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_apps__eq__Abs__conv_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_lift__subst_0)).
% 1.00/1.61 cnf(cls_apps__eq__Abs__conv_1, axiom, (X2=c_List_Olist_ONil(tc_Lambda_OdB)|c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_apps__eq__Abs__conv_1)).
% 1.00/1.61 cnf(cls_Var__eq__apps__conv_1, axiom, (X3=c_List_Olist_ONil(tc_Lambda_OdB)|c_Lambda_OdB_OVar(X1)!=c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Var__eq__apps__conv_1)).
% 1.00/1.61 cnf(cls_Abs__eq__apps__conv_1, axiom, (X3=c_List_Olist_ONil(tc_Lambda_OdB)|c_Lambda_OdB_OAbs(X1)!=c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Abs__eq__apps__conv_1)).
% 1.00/1.61 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)|~c_Type_Otyping(X6,X4,X1)|~hBOOL(hAPP(c_InductTermi_OIT,X4))|~c_Type_Otyping(c_Type_Oshift(X6,X5,X1,tc_Type_Otype),X3,X7)|~hBOOL(hAPP(c_InductTermi_OIT,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_MI1_0)).
% 1.00/1.61 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)|~c_Type_Otyping(X6,X4,X2)|~hBOOL(hAPP(c_InductTermi_OIT,X4))|~c_Type_Otyping(c_Type_Oshift(X6,X5,X2,tc_Type_Otype),X3,X7)|~hBOOL(hAPP(c_InductTermi_OIT,X3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_MI2_0)).
% 1.00/1.61 cnf(cls_App__eq__foldl__conv_4, axiom, (hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_App__eq__foldl__conv_4)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_lift__subst__lt_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_subst__preserves__beta_0)).
% 1.00/1.61 cnf(cls_apps__eq__Abs__conv_2, axiom, (c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_apps__eq__Abs__conv_2)).
% 1.00/1.61 cnf(cls_Var__eq__apps__conv_2, axiom, (c_Lambda_OdB_OVar(X1)=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Var__eq__apps__conv_2)).
% 1.00/1.61 cnf(cls_Abs__eq__apps__conv_2, axiom, (c_Lambda_OdB_OAbs(X1)=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Abs__eq__apps__conv_2)).
% 1.00/1.61 cnf(cls_foldr_Osimps_I1_J_0, axiom, (c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4)=X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_foldr_Osimps_I1_J_0)).
% 1.00/1.61 cnf(cls_foldl__Nil_0, axiom, (c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3)=X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_foldl__Nil_0)).
% 1.00/1.61 cnf(cls_subst__lemma_0, axiom, (c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4),X6)|~c_Type_Otyping(X1,X2,X3)|~c_Type_Otyping(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_subst__lemma_0)).
% 1.00/1.61 cnf(cls_Abs_0, axiom, (c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),hAPP(hAPP(c_Type_Otype_OFun,X3),X4))|~c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_Type_Otype),X2,X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Abs_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_nat__diff__split_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_nat__diff__split__asm_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_subst__App_0)).
% 1.00/1.61 cnf(cls_conjecture_1, negated_conjecture, (v_thesis____|~c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_conjecture_1)).
% 1.00/1.61 cnf(cls_that_0, axiom, (v_thesis____|~c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_that_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_beta_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_subst__Abs_0)).
% 1.00/1.61 cnf(cls_typing__elims_I2_J_1, axiom, (c_Type_Otyping(X1,X2,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X4,X2))|~c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_typing__elims_I2_J_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__semiring_Osemiring__rules_I20_J_0)).
% 1.00/1.61 cnf(cls_shift__lt_0, axiom, (hAPP(c_Type_Oshift(X1,X2,X3,X4),X5)=hAPP(X1,c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat))|~c_HOL_Oord__class_Oless(X2,X5,tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_shift__lt_0)).
% 1.00/1.61 cnf(cls_lift__type_0, axiom, (c_Type_Otyping(c_Type_Oshift(X1,X2,X3,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X4),X2),X5)|~c_Type_Otyping(X1,X4,X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_lift__type_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_appR_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_appL_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_lift__preserves__beta_0)).
% 1.00/1.61 cnf(cls_shift__gt_0, axiom, (hAPP(c_Type_Oshift(X1,X2,X3,X4),X5)=hAPP(X1,X5)|~c_HOL_Oord__class_Oless(X5,X2,tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_shift__gt_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__semiring_Osemiring__rules_I23_J_0)).
% 1.00/1.61 cnf(cls_shift__eq_0, axiom, (hAPP(c_Type_Oshift(X1,X2,X3,X4),X2)=X3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_shift__eq_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_nat__diff__split_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_liftn_Osimps_I2_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__less__cancel__right_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__less__cancel__left_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_subst__Var__IT_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__strict__mono_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_lift_Osimps_I2_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__less__mono2_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_nat__add__left__cancel__less_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_comm__monoid__add_Omult__assoc_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__semiring_Osemiring__rules_I21_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_ab__semigroup__add__class_Oadd__ac_I1_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__semiring_Osemiring__rules_I25_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__semiring_Oadd__a_0)).
% 1.00/1.61 cnf(cls_App_0, axiom, (c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)|~c_Type_Otyping(X1,X3,X5)|~c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X5),X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_App_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__less__mono_0)).
% 1.00/1.61 cnf(cls_map__is__Nil__conv_0, axiom, (X2=c_List_Olist_ONil(X3)|c_List_Omap(X1,X2,X3,X4)!=c_List_Olist_ONil(X4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_map__is__Nil__conv_0)).
% 1.00/1.61 cnf(cls_Nil__is__map__conv_0, axiom, (X3=c_List_Olist_ONil(X4)|c_List_Olist_ONil(X1)!=c_List_Omap(X2,X3,X4,X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Nil__is__map__conv_0)).
% 1.00/1.61 cnf(cls_not__Nil__step1_0, axiom, (~c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_not__Nil__step1_0)).
% 1.00/1.61 cnf(cls_not__step1__Nil_0, axiom, (~c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_not__step1__Nil_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__diff__conv_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__cancel__21_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__diff__conv_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_subst__lift_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_liftn_Osimps_I3_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_nat__add__assoc_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__neg__neg_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__pos__pos_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__less__cancel__left_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__strict__left__mono_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__less__cancel__right_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__strict__right__mono_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_pos__add__strict_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__gr__0_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__less_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__iff__diff__less__0_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_zero__less__double__add__iff__zero__less__single__add_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_double__add__less__zero__iff__single__less__zero_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_even__less__0__iff_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__eqI_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__eqI_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_nat__add__left__cancel__less_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__less__mono1_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_lift_Osimps_I3_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_comm__monoid__add_Omult__left__commute_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__semiring_Osemiring__rules_I22_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__cancel__21_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__commute_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_subst__Var_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_subst__gt_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_zero__less__diff_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__diff__left_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__cancel_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__cancel2_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__add__eq__less_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__lessD1_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__add__cancel_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_nat__add__left__commute_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_double__add__less__zero__iff__single__less__zero_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_even__less__0__iff_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_zero__less__double__add__iff__zero__less__single__add_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__iff__diff__less__0_0)).
% 1.00/1.61 cnf(cls_subject__reduction_0, axiom, (c_Type_Otyping(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Lambda_Obeta,X4),X2))|~c_Type_Otyping(X1,X4,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_subject__reduction_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_of__nat__aux_Osimps_I1_J_0)).
% 1.00/1.61 cnf(cls_map__is__Nil__conv_1, axiom, (c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3)=c_List_Olist_ONil(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_map__is__Nil__conv_1)).
% 1.00/1.61 cnf(cls_Nil__is__map__conv_1, axiom, (c_List_Olist_ONil(X1)=c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Nil__is__map__conv_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_zero__less__diff_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_of__nat__add_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__imp__diff__less_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_app__Var__IT_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__gr__0_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__gr__0_2)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_order__less__trans_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_xt1_I10_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_abs_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_of__nat__less__iff_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_termination__basic__simps_I1_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_trans__less__add1_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_termination__basic__simps_I2_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_trans__less__add2_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_not__add__less1_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_not__add__less2_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_lift__IT_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_liftn_Osimps_I1_J_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_zero__less__two_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__diff__inverse_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_lift_Osimps_I1_J_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_of__nat__0__less__iff_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_subst__lt_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_of__nat__less__iff_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_nat__less__cases_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_of__nat__0__less__iff_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__ringb_Oadd__cancel_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_eq__eqI_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_eq__eqI_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_not__less__iff__gr__or__eq_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_order__less__asym_H_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_order__less__asym_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_xt1_I9_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diffs0__imp__equal_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_less__add__one_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__right__cancel_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__left__cancel_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__imp__eq_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_subst__Var_2)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__diff__cancel_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_subst__Var_1)).
% 1.00/1.61 cnf(cls_beta__cases_I1_J_0, axiom, (~hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_beta__cases_I1_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_liftn_Osimps_I1_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_nat__add__right__cancel_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_nat__add__left__cancel_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_natgb_Oadd__cancel_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__add__0_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__add__inverse_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__add__inverse2_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_of__nat__less__0__iff_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_lift_Osimps_I1_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_linorder__antisym__conv3_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_linorder__less__linear_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_linorder__neqE_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_not__less__iff__gr__or__eq_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_linorder__neqE__ordered__idom_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_type_Osimps_I2_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_dB_Osimps_I2_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_type_Osimps_I2_J_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_dB_Osimps_I2_J_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_not__one__less__zero_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_comm__monoid__add_Omult__commute_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__semiring_Osemiring__rules_I24_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__semiring_Oadd__c_0)).
% 1.00/1.61 cnf(cls_subst__eq_0, axiom, (hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1)=X2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_subst__eq_0)).
% 1.00/1.61 cnf(cls_typing__elims_I1_J_0, axiom, (hAPP(X1,X2)=X3|~c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_typing__elims_I1_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_linorder__neqE__nat_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_nat__neq__iff_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__ringb_Osubr0__iff_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__ringb_Oadd__r0__iff_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_eq__iff__diff__eq__0_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_right__minus__eq_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_double__eq__0__iff_0)).
% 1.00/1.61 cnf(cls_linorder__neq__iff_1, axiom, (~class_Orderings_Olinorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_linorder__neq__iff_1)).
% 1.00/1.61 cnf(cls_order__less__irrefl_0, axiom, (~class_Orderings_Opreorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_order__less__irrefl_0)).
% 1.00/1.61 cnf(cls_order__less__le_1, axiom, (~class_Orderings_Oorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_order__less__le_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_neq0__conv_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_nat__add__commute_0)).
% 1.00/1.61 cnf(cls_not__less0_0, axiom, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_not__less0_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_gr__implies__not0_0)).
% 1.00/1.61 cnf(cls_ATP__Linkup_Ofequal__imp__equal_0, axiom, (X1=X2|~c_fequal(X1,X2,X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_ATP__Linkup_Ofequal__imp__equal_0)).
% 1.00/1.61 cnf(cls_typing_OVar_0, axiom, (c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_typing_OVar_0)).
% 1.00/1.61 cnf(cls_less__not__refl_0, axiom, (~c_HOL_Oord__class_Oless(X1,X1,tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_less__not__refl_0)).
% 1.00/1.61 cnf(cls_nat__less__le_1, axiom, (~c_HOL_Oord__class_Oless(X1,X1,tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_nat__less__le_1)).
% 1.00/1.61 cnf(cls_Lambda_0, axiom, (hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))|~hBOOL(hAPP(c_InductTermi_OIT,X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Lambda_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_double__eq__0__iff_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__is__0_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__is__0_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__eq__self__zero_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_natgb_Oadd__r0__iff_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_zero__less__one_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__ringb_Oadd__r0__iff_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__ringb_Osubr0__iff_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_comm__monoid__add_Omult__1_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__semiring_Osemiring__rules_I5_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__semiring_Oadd__0_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__0__left_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__0__right_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_comm__monoid__add_Omult__1__right_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_class__semiring_Osemiring__rules_I6_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_monoid__add__class_Oadd__0__right_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_eq__iff__diff__eq__0_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_right__minus__eq_1)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__self_0)).
% 1.00/1.61 cnf(cls_dB_Osimps_I5_J_0, axiom, (hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)!=c_Lambda_OdB_OVar(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_dB_Osimps_I5_J_0)).
% 1.00/1.61 cnf(cls_dB_Osimps_I8_J_0, axiom, (hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)!=c_Lambda_OdB_OAbs(X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_dB_Osimps_I8_J_0)).
% 1.00/1.61 cnf(cls_dB_Osimps_I4_J_0, axiom, (c_Lambda_OdB_OVar(X1)!=hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_dB_Osimps_I4_J_0)).
% 1.00/1.61 cnf(cls_dB_Osimps_I9_J_0, axiom, (c_Lambda_OdB_OAbs(X1)!=hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_dB_Osimps_I9_J_0)).
% 1.00/1.61 cnf(cls_listsp_ONil_0, axiom, (c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_listsp_ONil_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_gr0I_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__0__eq__0_0)).
% 1.00/1.61 cnf(cls_liftn__0_0, axiom, (c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2)=X1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_liftn__0_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_add__is__0_2)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_minus__nat_Odiff__0_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_diff__self__eq__0_0)).
% 1.00/1.61 cnf(cls_ATP__Linkup_Oequal__imp__fequal_0, axiom, (c_fequal(X1,X1,X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_ATP__Linkup_Oequal__imp__fequal_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_of__nat__eq__iff_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_plus__nat_Oadd__0_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_Nat_Oadd__0__right_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_natgb_Oadd__r0__iff_1)).
% 1.00/1.61 cnf(cls_uT_0, axiom, (c_Type_Otyping(v_e____,v_u____,v_T____)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_uT_0)).
% 1.00/1.61 cnf(cls_Var_I4_J_0, axiom, (c_Type_Otyping(v_ea______,v_ua______,v_T____)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Var_I4_J_0)).
% 1.00/1.61 cnf(cls_Var__IT_0, axiom, (hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Var__IT_0)).
% 1.00/1.61 cnf(clsarity_fun__Orderings_Opreorder, axiom, (class_Orderings_Opreorder(tc_fun(X1,X2))|~class_Orderings_Opreorder(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_fun__Orderings_Opreorder)).
% 1.00/1.61 cnf(clsarity_fun__Orderings_Oorder, axiom, (class_Orderings_Oorder(tc_fun(X1,X2))|~class_Orderings_Oorder(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_fun__Orderings_Oorder)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_of__nat__1_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_of__nat__0_0)).
% 1.00/1.61 cnf(cls_uIT_0, axiom, (hBOOL(hAPP(c_InductTermi_OIT,v_u____))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_uIT_0)).
% 1.00/1.61 cnf(cls_Var_I3_J_0, axiom, (hBOOL(hAPP(c_InductTermi_OIT,v_ua______))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_Var_I3_J_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_zero__neq__one_0)).
% 1.00/1.61 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/sandbox2/benchmark/theBenchmark.p', cls_one__neq__zero_0)).
% 1.00/1.61 cnf(cls_dB_Osimps_I1_J_0, axiom, (X1=X2|c_Lambda_OdB_OVar(X1)!=c_Lambda_OdB_OVar(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_dB_Osimps_I1_J_0)).
% 1.00/1.61 cnf(cls_dB_Osimps_I3_J_0, axiom, (X1=X2|c_Lambda_OdB_OAbs(X1)!=c_Lambda_OdB_OAbs(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_dB_Osimps_I3_J_0)).
% 1.00/1.61 cnf(cls_dB_Osimps_I6_J_0, axiom, (c_Lambda_OdB_OVar(X1)!=c_Lambda_OdB_OAbs(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_dB_Osimps_I6_J_0)).
% 1.00/1.61 cnf(cls_dB_Osimps_I7_J_0, axiom, (c_Lambda_OdB_OAbs(X1)!=c_Lambda_OdB_OVar(X2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_dB_Osimps_I7_J_0)).
% 1.00/1.61 cnf(clsarity_nat__Orderings_Olinorder, axiom, (class_Orderings_Olinorder(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__Orderings_Olinorder)).
% 1.00/1.61 cnf(clsarity_nat__Orderings_Opreorder, axiom, (class_Orderings_Opreorder(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__Orderings_Opreorder)).
% 1.00/1.61 cnf(clsarity_nat__Orderings_Oorder, axiom, (class_Orderings_Oorder(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__Orderings_Oorder)).
% 1.00/1.61 cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add, axiom, (class_OrderedGroup_Ocancel__semigroup__add(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__OrderedGroup_Ocancel__semigroup__add)).
% 1.00/1.61 cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, axiom, (class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add)).
% 1.00/1.61 cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add, axiom, (class_OrderedGroup_Ocomm__monoid__add(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__OrderedGroup_Ocomm__monoid__add)).
% 1.00/1.61 cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1, axiom, (class_Ring__and__Field_Ocomm__semiring__1(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__Ring__and__Field_Ocomm__semiring__1)).
% 1.00/1.61 cnf(clsarity_nat__OrderedGroup_Osemigroup__add, axiom, (class_OrderedGroup_Osemigroup__add(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__OrderedGroup_Osemigroup__add)).
% 1.00/1.61 cnf(clsarity_nat__Nat_Osemiring__char__0, axiom, (class_Nat_Osemiring__char__0(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__Nat_Osemiring__char__0)).
% 1.00/1.61 cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add, axiom, (class_OrderedGroup_Oab__semigroup__add(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__OrderedGroup_Oab__semigroup__add)).
% 1.00/1.61 cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, axiom, (class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le)).
% 1.00/1.61 cnf(clsarity_nat__OrderedGroup_Omonoid__add, axiom, (class_OrderedGroup_Omonoid__add(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__OrderedGroup_Omonoid__add)).
% 1.00/1.61 cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, axiom, (class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add)).
% 1.00/1.61 cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, axiom, (class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__OrderedGroup_Opordered__comm__monoid__add)).
% 1.00/1.61 cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one, axiom, (class_Ring__and__Field_Ozero__neq__one(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__Ring__and__Field_Ozero__neq__one)).
% 1.00/1.61 cnf(clsarity_nat__Ring__and__Field_Oordered__semidom, axiom, (class_Ring__and__Field_Oordered__semidom(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__Ring__and__Field_Oordered__semidom)).
% 1.00/1.61 cnf(clsarity_nat__Ring__and__Field_Osemiring__1, axiom, (class_Ring__and__Field_Osemiring__1(tc_nat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', clsarity_nat__Ring__and__Field_Osemiring__1)).
% 1.00/1.61 cnf(cls_conjecture_0, negated_conjecture, (~v_thesis____), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_conjecture_0)).
% 1.00/1.61 cnf(cls_False_0, axiom, (v_n____!=v_i____), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cls_False_0)).
% 1.00/1.61 cnf(i_0_367, 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).
% 1.00/1.61 cnf(i_0_368, 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).
% 1.00/1.61 cnf(i_0_369, 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).
% 1.00/1.61 cnf(i_0_370, 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).
% 1.00/1.61 cnf(i_0_371, 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).
% 1.00/1.61 cnf(i_0_372, axiom, (c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4)=c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),c_Suc(X2),X3,X4)), cls_shift__commute_0).
% 1.00/1.61 cnf(i_0_373, 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).
% 1.00/1.61 cnf(i_0_374, 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).
% 1.00/1.61 cnf(i_0_375, 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).
% 1.00/1.61 cnf(i_0_376, 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).
% 1.00/1.61 cnf(i_0_377, 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).
% 1.00/1.61 cnf(i_0_378, 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).
% 1.00/1.61 cnf(i_0_379, 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).
% 1.00/1.61 cnf(i_0_380, 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).
% 1.00/1.61 cnf(i_0_381, 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).
% 1.00/1.61 cnf(i_0_382, 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).
% 1.00/1.61 cnf(i_0_383, 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).
% 1.00/1.61 cnf(i_0_384, 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).
% 1.00/1.61 cnf(i_0_385, 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).
% 1.00/1.61 cnf(i_0_386, 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).
% 1.00/1.61 cnf(i_0_387, 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).
% 1.00/1.61 cnf(i_0_388, 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).
% 1.00/1.61 cnf(i_0_389, 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).
% 1.00/1.61 cnf(i_0_390, 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).
% 1.00/1.61 cnf(i_0_391, 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).
% 1.00/1.61 cnf(i_0_392, 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).
% 1.00/1.61 cnf(i_0_393, 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).
% 1.00/1.61 cnf(i_0_394, 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).
% 1.00/1.61 cnf(i_0_395, 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).
% 1.00/1.61 cnf(i_0_396, 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).
% 1.00/1.61 cnf(i_0_397, 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).
% 1.00/1.61 cnf(i_0_398, 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).
% 1.00/1.61 cnf(i_0_399, 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).
% 1.00/1.61 cnf(i_0_400, 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).
% 1.00/1.61 cnf(i_0_401, 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).
% 1.00/1.61 cnf(i_0_402, 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).
% 1.00/1.61 cnf(i_0_403, 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).
% 1.00/1.61 cnf(i_0_404, 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).
% 1.00/1.61 cnf(i_0_405, 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).
% 1.00/1.61 cnf(i_0_406, 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).
% 1.00/1.61 cnf(i_0_407, 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).
% 1.00/1.61 cnf(i_0_408, 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).
% 1.00/1.61 cnf(i_0_409, 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).
% 1.00/1.61 cnf(i_0_410, 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).
% 1.00/1.61 cnf(i_0_411, 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).
% 1.00/1.61 cnf(i_0_412, 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).
% 1.00/1.61 cnf(i_0_413, 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).
% 1.00/1.61 cnf(i_0_414, 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).
% 1.00/1.61 cnf(i_0_415, 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).
% 1.00/1.61 cnf(i_0_416, 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).
% 1.00/1.61 cnf(i_0_417, 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).
% 1.00/1.61 cnf(i_0_418, 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).
% 1.00/1.61 cnf(i_0_419, 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).
% 1.00/1.61 cnf(i_0_420, 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).
% 1.00/1.61 cnf(i_0_421, 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).
% 1.00/1.61 cnf(i_0_422, 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).
% 1.00/1.61 cnf(i_0_423, axiom, (X1=X2|c_Suc(X1)!=c_Suc(X2)), cls_Suc__inject_0).
% 1.00/1.61 cnf(i_0_424, axiom, (X1=X2|c_Suc(X1)!=c_Suc(X2)), cls_nat_Oinject_0).
% 1.00/1.61 cnf(i_0_425, axiom, (c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=X1), cls_diff__Suc__1_0).
% 1.00/1.61 cnf(i_0_426, axiom, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat)), cls_gr0__conv__Suc_1).
% 1.00/1.61 cnf(i_0_427, axiom, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat)), cls_zero__less__Suc_0).
% 1.00/1.61 cnf(i_0_428, axiom, (c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)), cls_lessI_0).
% 1.00/1.61 cnf(i_0_429, axiom, (c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)), cls_less__Suc__eq_2).
% 1.00/1.61 cnf(i_0_430, 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).
% 1.00/1.61 cnf(i_0_431, axiom, (c_Suc(X1)!=c_HOL_Ozero__class_Ozero(tc_nat)), cls_nat_Osimps_I3_J_0).
% 1.00/1.61 cnf(i_0_432, axiom, (c_Suc(X1)!=c_HOL_Ozero__class_Ozero(tc_nat)), cls_Suc__neq__Zero_0).
% 1.00/1.61 cnf(i_0_433, axiom, (c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(X1)), cls_nat_Osimps_I2_J_0).
% 1.00/1.61 cnf(i_0_434, axiom, (c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(X1)), cls_Zero__neq__Suc_0).
% 1.00/1.61 cnf(i_0_435, axiom, (c_Suc(X1)!=X1), cls_Suc__n__not__n_0).
% 1.00/1.61 cnf(i_0_436, axiom, (X1!=c_Suc(X1)), cls_n__not__Suc__n_0).
% 1.00/1.61 cnf(i_0_437, axiom, (c_HOL_Oone__class_Oone(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))), cls_One__nat__def_0).
% 1.00/1.61 cnf(i_0_438, 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(c_COMBC(c_COMBC(c_Lambda_Osubst,X3,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X4,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)), cls_subst__map_0, ['final']).
% 1.00/1.61 cnf(i_0_439, 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)|~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)|~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']).
% 1.00/1.61 cnf(i_0_440, 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']).
% 1.00/1.61 cnf(i_0_441, axiom, (c_Type_Otypings(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,X2,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)|~c_Type_Otypings(c_Type_Oshift(X1,X3,X6,tc_Type_Otype),X4,X5)|~c_Type_Otyping(X1,X2,X6)), cls_substs__lemma_0, ['final']).
% 1.00/1.61 cnf(i_0_442, axiom, (c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__types__1__1(X3,X4,X1,X2))|~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)|~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']).
% 1.00/1.61 cnf(i_0_443, 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']).
% 1.00/1.61 cnf(i_0_444, 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']).
% 1.00/1.61 cnf(i_0_445, 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']).
% 1.00/1.61 cnf(i_0_446, 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']).
% 1.00/1.61 cnf(i_0_447, 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(c_COMBC(c_Lambda_Olift,X3,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)), cls_lift__map_0, ['final']).
% 1.00/1.61 cnf(i_0_448, axiom, (X1=X2|~c_Type_Otyping(X3,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB),X2)|~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']).
% 1.00/1.61 cnf(i_0_449, axiom, (c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X2,X4),X3,tc_Type_Otype,tc_Type_Otype))|~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']).
% 1.00/1.61 cnf(i_0_450, axiom, (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))|~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']).
% 1.00/1.61 cnf(i_0_451, axiom, (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))|~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']).
% 1.00/1.61 cnf(i_0_452, axiom, (c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)|~c_Type_Otypings(X1,X3,X5)|~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']).
% 1.00/1.61 cnf(i_0_453, axiom, (c_Type_Otypings(c_Type_Oshift(X1,X2,X3,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X2,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X4,tc_Lambda_OdB,tc_Lambda_OdB),X5)|~c_Type_Otypings(X1,X4,X5)), cls_lift__types_0, ['final']).
% 1.00/1.61 cnf(i_0_454, axiom, (c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),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']).
% 1.00/1.61 cnf(i_0_455, 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']).
% 1.00/1.61 cnf(i_0_456, axiom, (c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X3,X1,X4,X2))|~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']).
% 1.00/1.61 cnf(i_0_457, axiom, (c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X1,X4,X2))|~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']).
% 1.00/1.61 cnf(i_0_458, axiom, (c_Type_Otypings(X1,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X3,X1,X4,X2))|~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']).
% 1.00/1.61 cnf(i_0_459, 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_367, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_460, 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']).
% 1.00/1.61 cnf(i_0_461, 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']).
% 1.00/1.61 cnf(i_0_462, 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']).
% 1.00/1.61 cnf(i_0_463, 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']).
% 1.00/1.61 cnf(i_0_464, 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']).
% 1.00/1.61 cnf(i_0_465, 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']).
% 1.00/1.61 cnf(i_0_466, 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']).
% 1.00/1.61 cnf(i_0_467, 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']).
% 1.00/1.61 cnf(i_0_468, 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']).
% 1.00/1.61 cnf(i_0_469, axiom, (c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)), cls_CHAINED_0, ['final']).
% 1.00/1.61 cnf(i_0_470, axiom, (c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)), cls_nT_0, ['final']).
% 1.00/1.61 cnf(i_0_471, axiom, (c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______)), cls_Var_I2_J_0, ['final']).
% 1.00/1.61 cnf(i_0_472, axiom, (c_Nat_Osemiring__1__class_Oof__nat(X2,X1)=c_Nat_Osemiring__1__class_Oof__nat__aux(c_COMBC(c_HOL_Oplus__class_Oplus(X1),c_HOL_Oone__class_Oone(X1),X1,X1,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']).
% 1.00/1.61 cnf(i_0_473, 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_369, c_0_370]), c_0_370]), c_0_370]), ['final']).
% 1.00/1.61 cnf(i_0_474, axiom, (hAPP(c_COMBC(X1,X2,X3,X4,X5),X6)=hAPP(hAPP(X1,X6),X2)), cls_COMBC__def_0, ['final']).
% 1.00/1.61 cnf(i_0_475, 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']).
% 1.00/1.61 cnf(i_0_476, 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']).
% 1.00/1.61 cnf(i_0_477, axiom, (c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X2,X4)),X3))|~c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X4),X3)), cls_typing__elims_I2_J_0, ['final']).
% 1.00/1.61 cnf(i_0_478, axiom, (hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)=X3|hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)!=c_List_Ofoldl(c_Lambda_OdB_OApp,X3,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)), cls_App__eq__foldl__conv_0, ['final']).
% 1.00/1.61 cnf(i_0_479, 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']).
% 1.00/1.61 cnf(i_0_480, 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_371, c_0_370]), c_0_370]), ['final']).
% 1.00/1.61 cnf(i_0_481, 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']).
% 1.00/1.61 cnf(i_0_482, 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']).
% 1.00/1.61 cnf(i_0_483, 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']).
% 1.00/1.61 cnf(i_0_484, 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']).
% 1.00/1.61 cnf(i_0_485, axiom, (X2=c_List_Olist_ONil(tc_Lambda_OdB)|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_1, ['final']).
% 1.00/1.61 cnf(i_0_486, axiom, (X3=c_List_Olist_ONil(tc_Lambda_OdB)|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_1, ['final']).
% 1.00/1.61 cnf(i_0_487, axiom, (X3=c_List_Olist_ONil(tc_Lambda_OdB)|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_1, ['final']).
% 1.00/1.61 cnf(i_0_488, plain, (c_Type_Oshift(c_Type_Oshift(X1,X2,X3,X4),c_HOL_Ozero__class_Ozero(tc_nat),X5,X4)=c_Type_Oshift(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X5,X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X3,X4)), inference(rw,[status(thm)],[i_0_372, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_489, 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)|~c_Type_Otyping(X6,X4,X1)|~hBOOL(hAPP(c_InductTermi_OIT,X4))|~c_Type_Otyping(c_Type_Oshift(X6,X5,X1,tc_Type_Otype),X3,X7)|~hBOOL(hAPP(c_InductTermi_OIT,X3))), cls_MI1_0, ['final']).
% 1.00/1.61 cnf(i_0_490, 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)|~c_Type_Otyping(X6,X4,X2)|~hBOOL(hAPP(c_InductTermi_OIT,X4))|~c_Type_Otyping(c_Type_Oshift(X6,X5,X2,tc_Type_Otype),X3,X7)|~hBOOL(hAPP(c_InductTermi_OIT,X3))), cls_MI2_0, ['final']).
% 1.00/1.61 cnf(i_0_491, axiom, (hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)), cls_App__eq__foldl__conv_4, ['final']).
% 1.00/1.61 cnf(i_0_492, 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']).
% 1.00/1.61 cnf(i_0_493, 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']).
% 1.00/1.61 cnf(i_0_494, axiom, (c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(X1)), cls_apps__eq__Abs__conv_2, ['final']).
% 1.00/1.61 cnf(i_0_495, axiom, (c_Lambda_OdB_OVar(X1)=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)), cls_Var__eq__apps__conv_2, ['final']).
% 1.00/1.61 cnf(i_0_496, axiom, (c_Lambda_OdB_OAbs(X1)=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)), cls_Abs__eq__apps__conv_2, ['final']).
% 1.00/1.61 cnf(i_0_497, axiom, (c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4)=X3), cls_foldr_Osimps_I1_J_0, ['final']).
% 1.00/1.61 cnf(i_0_498, axiom, (c_List_Ofoldl(X1,X2,c_List_Olist_ONil(X3),X4,X3)=X2), cls_foldl__Nil_0, ['final']).
% 1.00/1.61 cnf(i_0_499, axiom, (c_Type_Otyping(X1,hAPP(hAPP(hAPP(c_Lambda_Osubst,X5),X2),X4),X6)|~c_Type_Otyping(X1,X2,X3)|~c_Type_Otyping(c_Type_Oshift(X1,X4,X3,tc_Type_Otype),X5,X6)), cls_subst__lemma_0, ['final']).
% 1.00/1.61 cnf(i_0_500, 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_373, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_501, axiom, (c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X2),hAPP(hAPP(c_Type_Otype_OFun,X3),X4))|~c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_Type_Otype),X2,X4)), cls_Abs_0, ['final']).
% 1.00/1.61 cnf(i_0_502, 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']).
% 1.00/1.61 cnf(i_0_503, 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']).
% 1.00/1.61 cnf(i_0_504, 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']).
% 1.00/1.61 cnf(i_0_505, negated_conjecture, (v_thesis____|~c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,X1)), cls_conjecture_1, ['final']).
% 1.00/1.61 cnf(i_0_506, axiom, (v_thesis____|~c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,X1)), cls_that_0, ['final']).
% 1.00/1.61 cnf(i_0_507, 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']).
% 1.00/1.61 cnf(i_0_508, 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']).
% 1.00/1.61 cnf(i_0_509, 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_374, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_510, axiom, (c_Type_Otyping(X1,X2,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X1,X4,X2))|~c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X4),X2),X3)), cls_typing__elims_I2_J_1, ['final']).
% 1.00/1.61 cnf(i_0_511, 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']).
% 1.00/1.61 cnf(i_0_512, axiom, (hAPP(c_Type_Oshift(X1,X2,X3,X4),X5)=hAPP(X1,c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_nat),tc_nat))|~c_HOL_Oord__class_Oless(X2,X5,tc_nat)), cls_shift__lt_0, ['final']).
% 1.00/1.61 cnf(i_0_513, axiom, (c_Type_Otyping(c_Type_Oshift(X1,X2,X3,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X4),X2),X5)|~c_Type_Otyping(X1,X4,X5)), cls_lift__type_0, ['final']).
% 1.00/1.61 cnf(i_0_514, 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_375, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_515, 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']).
% 1.00/1.61 cnf(i_0_516, 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']).
% 1.00/1.61 cnf(i_0_517, 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']).
% 1.00/1.61 cnf(i_0_518, 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_376, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_519, axiom, (hAPP(c_Type_Oshift(X1,X2,X3,X4),X5)=hAPP(X1,X5)|~c_HOL_Oord__class_Oless(X5,X2,tc_nat)), cls_shift__gt_0, ['final']).
% 1.00/1.61 cnf(i_0_520, 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_377, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_521, 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_378, c_0_370]), ['final']).
% 1.00/1.61 cnf(i_0_522, 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']).
% 1.00/1.61 cnf(i_0_523, 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_379, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_524, 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_380, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_525, 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_381, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_526, axiom, (hAPP(c_Type_Oshift(X1,X2,X3,X4),X2)=X3), cls_shift__eq_0, ['final']).
% 1.00/1.61 cnf(i_0_527, 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']).
% 1.00/1.61 cnf(i_0_528, 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']).
% 1.00/1.61 cnf(i_0_529, 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']).
% 1.00/1.61 cnf(i_0_530, 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']).
% 1.00/1.61 cnf(i_0_531, 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_382, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_532, 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']).
% 1.00/1.61 cnf(i_0_533, 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_383, c_0_370]), ['final']).
% 1.00/1.61 cnf(i_0_534, 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_384, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_535, 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']).
% 1.00/1.61 cnf(i_0_536, 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_385, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_537, 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']).
% 1.00/1.61 cnf(i_0_538, 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']).
% 1.00/1.61 cnf(i_0_539, 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']).
% 1.00/1.61 cnf(i_0_540, 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']).
% 1.00/1.61 cnf(i_0_541, 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']).
% 1.00/1.61 cnf(i_0_542, 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']).
% 1.00/1.61 cnf(i_0_543, 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']).
% 1.00/1.61 cnf(i_0_544, 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']).
% 1.00/1.61 cnf(i_0_545, 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_386, c_0_370]), ['final']).
% 1.00/1.61 cnf(i_0_546, axiom, (c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)|~c_Type_Otyping(X1,X3,X5)|~c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X5),X4))), cls_App_0, ['final']).
% 1.00/1.61 cnf(i_0_547, 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']).
% 1.00/1.61 cnf(i_0_548, 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_387, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_549, axiom, (X2=c_List_Olist_ONil(X3)|c_List_Omap(X1,X2,X3,X4)!=c_List_Olist_ONil(X4)), cls_map__is__Nil__conv_0, ['final']).
% 1.00/1.61 cnf(i_0_550, axiom, (X3=c_List_Olist_ONil(X4)|c_List_Olist_ONil(X1)!=c_List_Omap(X2,X3,X4,X1)), cls_Nil__is__map__conv_0, ['final']).
% 1.00/1.61 cnf(i_0_551, axiom, (~c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2)), cls_not__Nil__step1_0, ['final']).
% 1.00/1.61 cnf(i_0_552, axiom, (~c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3)), cls_not__step1__Nil_0, ['final']).
% 1.00/1.61 cnf(i_0_553, 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_388, c_0_370]), ['final']).
% 1.00/1.61 cnf(i_0_554, 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']).
% 1.00/1.61 cnf(i_0_555, 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']).
% 1.00/1.61 cnf(i_0_556, 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']).
% 1.00/1.61 cnf(i_0_557, 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_389, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_558, axiom, (hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X1),X2)),X3),X2)=X1), cls_subst__lift_0, ['final']).
% 1.00/1.61 cnf(i_0_559, 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_390, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_560, 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']).
% 1.00/1.61 cnf(i_0_561, 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']).
% 1.00/1.61 cnf(i_0_562, 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']).
% 1.00/1.61 cnf(i_0_563, 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']).
% 1.00/1.61 cnf(i_0_564, 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_391, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_565, 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_392, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_566, 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']).
% 1.00/1.61 cnf(i_0_567, 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']).
% 1.00/1.61 cnf(i_0_568, 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']).
% 1.00/1.61 cnf(i_0_569, 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']).
% 1.00/1.61 cnf(i_0_570, 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']).
% 1.00/1.61 cnf(i_0_571, 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']).
% 1.00/1.61 cnf(i_0_572, 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']).
% 1.00/1.61 cnf(i_0_573, 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_393, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_574, 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_394, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_575, 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']).
% 1.00/1.61 cnf(i_0_576, 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']).
% 1.00/1.61 cnf(i_0_577, 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']).
% 1.00/1.61 cnf(i_0_578, 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']).
% 1.00/1.61 cnf(i_0_579, 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_395, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_580, 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_396, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_581, 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']).
% 1.00/1.61 cnf(i_0_582, 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']).
% 1.00/1.61 cnf(i_0_583, 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_397, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_584, 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_398, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_585, 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']).
% 1.00/1.61 cnf(i_0_586, 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']).
% 1.00/1.61 cnf(i_0_587, 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']).
% 1.00/1.61 cnf(i_0_588, 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']).
% 1.00/1.61 cnf(i_0_589, 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']).
% 1.00/1.61 cnf(i_0_590, 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']).
% 1.00/1.61 cnf(i_0_591, 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']).
% 1.00/1.61 cnf(i_0_592, 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_399, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_593, 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']).
% 1.00/1.61 cnf(i_0_594, 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']).
% 1.00/1.61 cnf(i_0_595, 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']).
% 1.00/1.61 cnf(i_0_596, 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']).
% 1.00/1.61 cnf(i_0_597, 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_400, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_598, 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_401, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_599, 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_402, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_600, 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_403, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_601, 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_404, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_602, 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']).
% 1.00/1.61 cnf(i_0_603, 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']).
% 1.00/1.61 cnf(i_0_604, 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_405, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_605, 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']).
% 1.00/1.61 cnf(i_0_606, 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']).
% 1.00/1.61 cnf(i_0_607, 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']).
% 1.00/1.61 cnf(i_0_608, 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_406, c_0_368]), c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_609, 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_407, c_0_368]), c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_610, 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']).
% 1.00/1.61 cnf(i_0_611, 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']).
% 1.00/1.61 cnf(i_0_612, 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']).
% 1.00/1.61 cnf(i_0_613, 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']).
% 1.00/1.61 cnf(i_0_614, 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']).
% 1.00/1.61 cnf(i_0_615, axiom, (c_Type_Otyping(X1,X2,X3)|~hBOOL(hAPP(hAPP(c_Lambda_Obeta,X4),X2))|~c_Type_Otyping(X1,X4,X3)), cls_subject__reduction_0, ['final']).
% 1.00/1.61 cnf(i_0_616, 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']).
% 1.00/1.61 cnf(i_0_617, 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_408, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_618, axiom, (c_List_Omap(X1,c_List_Olist_ONil(X2),X2,X3)=c_List_Olist_ONil(X3)), cls_map__is__Nil__conv_1, ['final']).
% 1.00/1.61 cnf(i_0_619, axiom, (c_List_Olist_ONil(X1)=c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1)), cls_Nil__is__map__conv_1, ['final']).
% 1.00/1.61 cnf(i_0_620, 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_409, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_621, 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']).
% 1.00/1.61 cnf(i_0_622, 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']).
% 1.00/1.61 cnf(i_0_623, 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']).
% 1.00/1.61 cnf(i_0_624, 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']).
% 1.00/1.61 cnf(i_0_625, 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']).
% 1.00/1.61 cnf(i_0_626, 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']).
% 1.00/1.61 cnf(i_0_627, 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']).
% 1.00/1.61 cnf(i_0_628, 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']).
% 1.00/1.61 cnf(i_0_629, 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_410, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_630, 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']).
% 1.00/1.61 cnf(i_0_631, 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']).
% 1.00/1.61 cnf(i_0_632, 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']).
% 1.00/1.61 cnf(i_0_633, 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']).
% 1.00/1.61 cnf(i_0_634, 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']).
% 1.00/1.61 cnf(i_0_635, 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']).
% 1.00/1.61 cnf(i_0_636, 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']).
% 1.00/1.61 cnf(i_0_637, 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']).
% 1.00/1.61 cnf(i_0_638, 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_411, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_639, 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_412, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_640, 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_413, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_641, 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_414, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_642, 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_415, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_643, 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_416, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_644, axiom, (hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X1),X2)))|~hBOOL(hAPP(c_InductTermi_OIT,X1))), cls_lift__IT_0, ['final']).
% 1.00/1.61 cnf(i_0_645, 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']).
% 1.00/1.61 cnf(i_0_646, 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_417, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_647, 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']).
% 1.00/1.61 cnf(i_0_648, 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']).
% 1.00/1.61 cnf(i_0_649, 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']).
% 1.00/1.61 cnf(i_0_650, 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_418, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_651, 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_419, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_652, 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']).
% 1.00/1.61 cnf(i_0_653, 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']).
% 1.00/1.61 cnf(i_0_654, 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']).
% 1.00/1.61 cnf(i_0_655, 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']).
% 1.00/1.61 cnf(i_0_656, 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']).
% 1.00/1.61 cnf(i_0_657, 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']).
% 1.00/1.61 cnf(i_0_658, 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']).
% 1.00/1.61 cnf(i_0_659, 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']).
% 1.00/1.61 cnf(i_0_660, 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']).
% 1.00/1.61 cnf(i_0_661, 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']).
% 1.00/1.61 cnf(i_0_662, 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']).
% 1.00/1.61 cnf(i_0_663, 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']).
% 1.00/1.61 cnf(i_0_664, 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']).
% 1.00/1.61 cnf(i_0_665, 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']).
% 1.00/1.61 cnf(i_0_666, 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']).
% 1.00/1.61 cnf(i_0_667, 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']).
% 1.00/1.61 cnf(i_0_668, 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']).
% 1.00/1.61 cnf(i_0_669, 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']).
% 1.00/1.61 cnf(i_0_670, 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_420, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_671, 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_421, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_672, 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']).
% 1.00/1.61 cnf(i_0_673, 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']).
% 1.00/1.61 cnf(i_0_674, 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_422, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_675, axiom, (~hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2))), cls_beta__cases_I1_J_0, ['final']).
% 1.00/1.61 cnf(i_0_676, 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_423, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_677, 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_424, c_0_368]), c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_678, 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_425, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_679, 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_426, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_680, 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_427, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_681, 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_428, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_682, 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_429, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_683, 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']).
% 1.00/1.61 cnf(i_0_684, 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']).
% 1.00/1.61 cnf(i_0_685, 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']).
% 1.00/1.61 cnf(i_0_686, 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']).
% 1.00/1.61 cnf(i_0_687, 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']).
% 1.00/1.61 cnf(i_0_688, 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']).
% 1.00/1.61 cnf(i_0_689, 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']).
% 1.00/1.61 cnf(i_0_690, 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']).
% 1.00/1.61 cnf(i_0_691, 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']).
% 1.00/1.61 cnf(i_0_692, 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']).
% 1.00/1.61 cnf(i_0_693, 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']).
% 1.00/1.61 cnf(i_0_694, 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']).
% 1.00/1.61 cnf(i_0_695, 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']).
% 1.00/1.61 cnf(i_0_696, 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']).
% 1.00/1.61 cnf(i_0_697, 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']).
% 1.00/1.61 cnf(i_0_698, 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']).
% 1.00/1.61 cnf(i_0_699, 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']).
% 1.00/1.61 cnf(i_0_700, 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']).
% 1.00/1.61 cnf(i_0_701, 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']).
% 1.00/1.61 cnf(i_0_702, 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']).
% 1.00/1.61 cnf(i_0_703, 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']).
% 1.00/1.61 cnf(i_0_704, 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']).
% 1.00/1.61 cnf(i_0_705, axiom, (hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1)=X2), cls_subst__eq_0, ['final']).
% 1.00/1.61 cnf(i_0_706, axiom, (hAPP(X1,X2)=X3|~c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3)), cls_typing__elims_I1_J_0, ['final']).
% 1.00/1.61 cnf(i_0_707, 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']).
% 1.00/1.61 cnf(i_0_708, 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']).
% 1.00/1.61 cnf(i_0_709, 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']).
% 1.00/1.61 cnf(i_0_710, 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']).
% 1.00/1.61 cnf(i_0_711, 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']).
% 1.00/1.61 cnf(i_0_712, 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']).
% 1.00/1.61 cnf(i_0_713, 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_430, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_714, 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']).
% 1.00/1.61 cnf(i_0_715, axiom, (~class_Orderings_Olinorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1)), cls_linorder__neq__iff_1, ['final']).
% 1.00/1.61 cnf(i_0_716, axiom, (~class_Orderings_Opreorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1)), cls_order__less__irrefl_0, ['final']).
% 1.00/1.61 cnf(i_0_717, axiom, (~class_Orderings_Oorder(X1)|~c_HOL_Oord__class_Oless(X2,X2,X1)), cls_order__less__le_1, ['final']).
% 1.00/1.61 cnf(i_0_718, 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']).
% 1.00/1.61 cnf(i_0_719, 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']).
% 1.00/1.61 cnf(i_0_720, axiom, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)), cls_not__less0_0, ['final']).
% 1.00/1.61 cnf(i_0_721, axiom, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)), cls_gr__implies__not0_0, ['final']).
% 1.00/1.61 cnf(i_0_722, axiom, (X1=X2|~c_fequal(X1,X2,X3)), cls_ATP__Linkup_Ofequal__imp__equal_0, ['final']).
% 1.00/1.61 cnf(i_0_723, axiom, (c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2))), cls_typing_OVar_0, ['final']).
% 1.00/1.61 cnf(i_0_724, axiom, (~c_HOL_Oord__class_Oless(X1,X1,tc_nat)), cls_less__not__refl_0, ['final']).
% 1.00/1.61 cnf(i_0_725, axiom, (~c_HOL_Oord__class_Oless(X1,X1,tc_nat)), cls_nat__less__le_1, ['final']).
% 1.00/1.61 cnf(i_0_726, axiom, (hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X1)))|~hBOOL(hAPP(c_InductTermi_OIT,X1))), cls_Lambda_0, ['final']).
% 1.00/1.61 cnf(i_0_727, 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']).
% 1.00/1.61 cnf(i_0_728, 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_431, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_729, 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_432, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_730, 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_433, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_731, 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_434, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_732, 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']).
% 1.00/1.61 cnf(i_0_733, 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']).
% 1.00/1.61 cnf(i_0_734, 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_435, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_735, 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_436, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_736, 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']).
% 1.00/1.61 cnf(i_0_737, 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']).
% 1.00/1.61 cnf(i_0_738, 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']).
% 1.00/1.61 cnf(i_0_739, 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']).
% 1.00/1.61 cnf(i_0_740, 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']).
% 1.00/1.61 cnf(i_0_741, 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']).
% 1.00/1.61 cnf(i_0_742, 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']).
% 1.00/1.61 cnf(i_0_743, 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']).
% 1.00/1.61 cnf(i_0_744, 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']).
% 1.00/1.61 cnf(i_0_745, 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']).
% 1.00/1.61 cnf(i_0_746, 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']).
% 1.00/1.61 cnf(i_0_747, 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']).
% 1.00/1.61 cnf(i_0_748, 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']).
% 1.00/1.61 cnf(i_0_749, 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']).
% 1.00/1.61 cnf(i_0_750, 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']).
% 1.00/1.61 cnf(i_0_751, 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']).
% 1.00/1.61 cnf(i_0_752, axiom, (hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)!=c_Lambda_OdB_OVar(X3)), cls_dB_Osimps_I5_J_0, ['final']).
% 1.00/1.61 cnf(i_0_753, axiom, (hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2)!=c_Lambda_OdB_OAbs(X3)), cls_dB_Osimps_I8_J_0, ['final']).
% 1.00/1.61 cnf(i_0_754, axiom, (c_Lambda_OdB_OVar(X1)!=hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)), cls_dB_Osimps_I4_J_0, ['final']).
% 1.00/1.61 cnf(i_0_755, axiom, (c_Lambda_OdB_OAbs(X1)!=hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)), cls_dB_Osimps_I9_J_0, ['final']).
% 1.00/1.61 cnf(i_0_756, axiom, (c_List_Olistsp(X1,c_List_Olist_ONil(X2),X2)), cls_listsp_ONil_0, ['final']).
% 1.00/1.61 cnf(i_0_757, 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']).
% 1.00/1.61 cnf(i_0_758, 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']).
% 1.00/1.61 cnf(i_0_759, axiom, (c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2)=X1), cls_liftn__0_0, ['final']).
% 1.00/1.61 cnf(i_0_760, 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']).
% 1.00/1.61 cnf(i_0_761, 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_437, c_0_368]), ['final']).
% 1.00/1.61 cnf(i_0_762, axiom, (c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=X1), cls_minus__nat_Odiff__0_0, ['final']).
% 1.00/1.61 cnf(i_0_763, axiom, (c_HOL_Ominus__class_Ominus(X1,X1,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)), cls_diff__self__eq__0_0, ['final']).
% 1.00/1.61 cnf(i_0_764, axiom, (c_fequal(X1,X1,X2)), cls_ATP__Linkup_Oequal__imp__fequal_0, ['final']).
% 1.00/1.61 cnf(i_0_765, 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']).
% 1.00/1.61 cnf(i_0_766, 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']).
% 1.00/1.61 cnf(i_0_767, 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']).
% 1.00/1.61 cnf(i_0_768, 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']).
% 1.00/1.61 cnf(i_0_769, axiom, (c_Type_Otyping(v_e____,v_u____,v_T____)), cls_uT_0, ['final']).
% 1.00/1.61 cnf(i_0_770, axiom, (c_Type_Otyping(v_ea______,v_ua______,v_T____)), cls_Var_I4_J_0, ['final']).
% 1.00/1.61 cnf(i_0_771, axiom, (hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X1)))), cls_Var__IT_0, ['final']).
% 1.00/1.61 cnf(i_0_772, axiom, (class_Orderings_Opreorder(tc_fun(X1,X2))|~class_Orderings_Opreorder(X2)), clsarity_fun__Orderings_Opreorder, ['final']).
% 1.00/1.61 cnf(i_0_773, axiom, (class_Orderings_Oorder(tc_fun(X1,X2))|~class_Orderings_Oorder(X2)), clsarity_fun__Orderings_Oorder, ['final']).
% 1.00/1.61 cnf(i_0_774, 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']).
% 1.00/1.61 cnf(i_0_775, 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']).
% 1.00/1.61 cnf(i_0_776, axiom, (hBOOL(hAPP(c_InductTermi_OIT,v_u____))), cls_uIT_0, ['final']).
% 1.00/1.61 cnf(i_0_777, axiom, (hBOOL(hAPP(c_InductTermi_OIT,v_ua______))), cls_Var_I3_J_0, ['final']).
% 1.00/1.61 cnf(i_0_778, 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']).
% 1.00/1.61 cnf(i_0_779, 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']).
% 1.00/1.61 cnf(i_0_780, axiom, (X1=X2|c_Lambda_OdB_OVar(X1)!=c_Lambda_OdB_OVar(X2)), cls_dB_Osimps_I1_J_0, ['final']).
% 1.00/1.61 cnf(i_0_781, axiom, (X1=X2|c_Lambda_OdB_OAbs(X1)!=c_Lambda_OdB_OAbs(X2)), cls_dB_Osimps_I3_J_0, ['final']).
% 1.00/1.61 cnf(i_0_782, axiom, (c_Lambda_OdB_OVar(X1)!=c_Lambda_OdB_OAbs(X2)), cls_dB_Osimps_I6_J_0, ['final']).
% 1.00/1.61 cnf(i_0_783, axiom, (c_Lambda_OdB_OAbs(X1)!=c_Lambda_OdB_OVar(X2)), cls_dB_Osimps_I7_J_0, ['final']).
% 1.00/1.61 cnf(i_0_784, axiom, (class_Orderings_Olinorder(tc_nat)), clsarity_nat__Orderings_Olinorder, ['final']).
% 1.00/1.61 cnf(i_0_785, axiom, (class_Orderings_Opreorder(tc_nat)), clsarity_nat__Orderings_Opreorder, ['final']).
% 1.00/1.61 cnf(i_0_786, axiom, (class_Orderings_Oorder(tc_nat)), clsarity_nat__Orderings_Oorder, ['final']).
% 1.00/1.61 cnf(i_0_787, axiom, (class_OrderedGroup_Ocancel__semigroup__add(tc_nat)), clsarity_nat__OrderedGroup_Ocancel__semigroup__add, ['final']).
% 1.00/1.61 cnf(i_0_788, axiom, (class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat)), clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, ['final']).
% 1.00/1.61 cnf(i_0_789, axiom, (class_OrderedGroup_Ocomm__monoid__add(tc_nat)), clsarity_nat__OrderedGroup_Ocomm__monoid__add, ['final']).
% 1.00/1.61 cnf(i_0_790, axiom, (class_Ring__and__Field_Ocomm__semiring__1(tc_nat)), clsarity_nat__Ring__and__Field_Ocomm__semiring__1, ['final']).
% 1.00/1.61 cnf(i_0_791, axiom, (class_OrderedGroup_Osemigroup__add(tc_nat)), clsarity_nat__OrderedGroup_Osemigroup__add, ['final']).
% 1.00/1.61 cnf(i_0_792, axiom, (class_Nat_Osemiring__char__0(tc_nat)), clsarity_nat__Nat_Osemiring__char__0, ['final']).
% 1.00/1.61 cnf(i_0_793, axiom, (class_OrderedGroup_Oab__semigroup__add(tc_nat)), clsarity_nat__OrderedGroup_Oab__semigroup__add, ['final']).
% 1.00/1.61 cnf(i_0_794, axiom, (class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat)), clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, ['final']).
% 1.00/1.61 cnf(i_0_795, axiom, (class_OrderedGroup_Omonoid__add(tc_nat)), clsarity_nat__OrderedGroup_Omonoid__add, ['final']).
% 1.00/1.61 cnf(i_0_796, axiom, (class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat)), clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, ['final']).
% 1.00/1.61 cnf(i_0_797, axiom, (class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)), clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, ['final']).
% 1.00/1.61 cnf(i_0_798, axiom, (class_Ring__and__Field_Ozero__neq__one(tc_nat)), clsarity_nat__Ring__and__Field_Ozero__neq__one, ['final']).
% 1.00/1.61 cnf(i_0_799, axiom, (class_Ring__and__Field_Oordered__semidom(tc_nat)), clsarity_nat__Ring__and__Field_Oordered__semidom, ['final']).
% 1.00/1.61 cnf(i_0_800, axiom, (class_Ring__and__Field_Osemiring__1(tc_nat)), clsarity_nat__Ring__and__Field_Osemiring__1, ['final']).
% 1.00/1.61 cnf(i_0_801, negated_conjecture, (~v_thesis____), cls_conjecture_0, ['final']).
% 1.00/1.61 cnf(i_0_802, axiom, (v_n____!=v_i____), cls_False_0, ['final']).
% 1.00/1.61 cnf(i_0_803, axiom, (X1=X1)).
% 1.00/1.61 cnf(i_0_804, axiom, (X1=X2|X2!=X1)).
% 1.00/1.61 cnf(i_0_805, axiom, (X1=X2|X1!=X3|X3!=X2)).
% 1.00/1.62 cnf(i_0_806, axiom, (X1!=X2|hAPP(X1,X3)=hAPP(X2,X3))).
% 1.00/1.62 cnf(i_0_807, axiom, (X1!=X2|hAPP(X3,X1)=hAPP(X3,X2))).
% 1.00/1.62 cnf(i_0_808, axiom, (X1!=X2|c_Type_Oshift(X1,X3,X4,X5)=c_Type_Oshift(X2,X3,X4,X5))).
% 1.00/1.62 cnf(i_0_809, axiom, (X1!=X2|c_Type_Oshift(X3,X1,X4,X5)=c_Type_Oshift(X3,X2,X4,X5))).
% 1.00/1.62 cnf(i_0_810, axiom, (X1!=X2|c_Type_Oshift(X3,X4,X1,X5)=c_Type_Oshift(X3,X4,X2,X5))).
% 1.00/1.62 cnf(i_0_811, axiom, (X1!=X2|c_Type_Oshift(X3,X4,X5,X1)=c_Type_Oshift(X3,X4,X5,X2))).
% 1.00/1.62 cnf(i_0_812, axiom, (X1!=X2|c_Lambda_OdB_OAbs(X1)=c_Lambda_OdB_OAbs(X2))).
% 1.00/1.62 cnf(i_0_813, axiom, (X1!=X2|c_HOL_Ozero__class_Ozero(X1)=c_HOL_Ozero__class_Ozero(X2))).
% 1.00/1.62 cnf(i_0_814, axiom, (X1!=X2|c_HOL_Oone__class_Oone(X1)=c_HOL_Oone__class_Oone(X2))).
% 1.00/1.62 cnf(i_0_815, axiom, (X1!=X2|c_Nat_Osemiring__1__class_Oof__nat(X1,X3)=c_Nat_Osemiring__1__class_Oof__nat(X2,X3))).
% 1.00/1.62 cnf(i_0_816, axiom, (X1!=X2|c_Nat_Osemiring__1__class_Oof__nat(X3,X1)=c_Nat_Osemiring__1__class_Oof__nat(X3,X2))).
% 1.00/1.62 cnf(i_0_817, 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))).
% 1.00/1.62 cnf(i_0_818, 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))).
% 1.00/1.62 cnf(i_0_819, 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))).
% 1.00/1.62 cnf(i_0_820, 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))).
% 1.00/1.62 cnf(i_0_821, axiom, (X1!=X2|c_List_Ofoldl(X1,X3,X4,X5,X6)=c_List_Ofoldl(X2,X3,X4,X5,X6))).
% 1.00/1.62 cnf(i_0_822, axiom, (X1!=X2|c_List_Ofoldl(X3,X1,X4,X5,X6)=c_List_Ofoldl(X3,X2,X4,X5,X6))).
% 1.00/1.62 cnf(i_0_823, axiom, (X1!=X2|c_List_Ofoldl(X3,X4,X1,X5,X6)=c_List_Ofoldl(X3,X4,X2,X5,X6))).
% 1.00/1.62 cnf(i_0_824, axiom, (X1!=X2|c_List_Ofoldl(X3,X4,X5,X1,X6)=c_List_Ofoldl(X3,X4,X5,X2,X6))).
% 1.00/1.62 cnf(i_0_825, axiom, (X1!=X2|c_List_Ofoldl(X3,X4,X5,X6,X1)=c_List_Ofoldl(X3,X4,X5,X6,X2))).
% 1.00/1.62 cnf(i_0_826, axiom, (X1!=X2|c_Lambda_Oliftn(X1,X3,X4)=c_Lambda_Oliftn(X2,X3,X4))).
% 1.00/1.62 cnf(i_0_827, axiom, (X1!=X2|c_Lambda_Oliftn(X3,X1,X4)=c_Lambda_Oliftn(X3,X2,X4))).
% 1.00/1.62 cnf(i_0_828, axiom, (X1!=X2|c_Lambda_Oliftn(X3,X4,X1)=c_Lambda_Oliftn(X3,X4,X2))).
% 1.00/1.62 cnf(i_0_829, axiom, (X1!=X2|c_List_Olist_ONil(X1)=c_List_Olist_ONil(X2))).
% 1.00/1.62 cnf(i_0_830, axiom, (X1!=X2|c_HOL_Ominus__class_Ominus(X1,X3,X4)=c_HOL_Ominus__class_Ominus(X2,X3,X4))).
% 1.00/1.62 cnf(i_0_831, axiom, (X1!=X2|c_HOL_Ominus__class_Ominus(X3,X1,X4)=c_HOL_Ominus__class_Ominus(X3,X2,X4))).
% 1.00/1.62 cnf(i_0_832, axiom, (X1!=X2|c_HOL_Ominus__class_Ominus(X3,X4,X1)=c_HOL_Ominus__class_Ominus(X3,X4,X2))).
% 1.00/1.62 cnf(i_0_833, axiom, (X1!=X2|c_List_Omap(X1,X3,X4,X5)=c_List_Omap(X2,X3,X4,X5))).
% 1.00/1.62 cnf(i_0_834, axiom, (X1!=X2|c_List_Omap(X3,X1,X4,X5)=c_List_Omap(X3,X2,X4,X5))).
% 1.00/1.62 cnf(i_0_835, axiom, (X1!=X2|c_List_Omap(X3,X4,X1,X5)=c_List_Omap(X3,X4,X2,X5))).
% 1.00/1.62 cnf(i_0_836, axiom, (X1!=X2|c_List_Omap(X3,X4,X5,X1)=c_List_Omap(X3,X4,X5,X2))).
% 1.00/1.62 cnf(i_0_837, axiom, (X1!=X2|c_List_Ofoldr(X1,X3,X4,X5,X6)=c_List_Ofoldr(X2,X3,X4,X5,X6))).
% 1.00/1.62 cnf(i_0_838, axiom, (X1!=X2|c_List_Ofoldr(X3,X1,X4,X5,X6)=c_List_Ofoldr(X3,X2,X4,X5,X6))).
% 1.00/1.62 cnf(i_0_839, axiom, (X1!=X2|c_List_Ofoldr(X3,X4,X1,X5,X6)=c_List_Ofoldr(X3,X4,X2,X5,X6))).
% 1.00/1.62 cnf(i_0_840, axiom, (X1!=X2|c_List_Ofoldr(X3,X4,X5,X1,X6)=c_List_Ofoldr(X3,X4,X5,X2,X6))).
% 1.00/1.62 cnf(i_0_841, axiom, (X1!=X2|c_List_Ofoldr(X3,X4,X5,X6,X1)=c_List_Ofoldr(X3,X4,X5,X6,X2))).
% 1.00/1.62 cnf(i_0_842, axiom, (X1!=X2|c_Lambda_OdB_OVar(X1)=c_Lambda_OdB_OVar(X2))).
% 1.00/1.62 cnf(i_0_843, axiom, (X1!=X2|~c_Type_Otyping(X1,X3,X4)|c_Type_Otyping(X2,X3,X4))).
% 1.00/1.62 cnf(i_0_844, axiom, (X1!=X2|~c_Type_Otyping(X3,X1,X4)|c_Type_Otyping(X3,X2,X4))).
% 1.00/1.62 cnf(i_0_845, axiom, (X1!=X2|~c_Type_Otyping(X3,X4,X1)|c_Type_Otyping(X3,X4,X2))).
% 1.00/1.62 cnf(i_0_846, axiom, (X1!=X2|~class_OrderedGroup_Oab__semigroup__add(X1)|class_OrderedGroup_Oab__semigroup__add(X2))).
% 1.00/1.63 cnf(i_0_847, axiom, (X1!=X2|~class_Ring__and__Field_Ocomm__semiring__1(X1)|class_Ring__and__Field_Ocomm__semiring__1(X2))).
% 1.00/1.63 cnf(i_0_848, axiom, (X1!=X2|~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)|class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2))).
% 1.00/1.63 cnf(i_0_849, axiom, (X1!=X2|~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)|class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2))).
% 1.00/1.63 cnf(i_0_850, axiom, (X1!=X2|~class_OrderedGroup_Ocomm__monoid__add(X1)|class_OrderedGroup_Ocomm__monoid__add(X2))).
% 1.00/1.63 cnf(i_0_851, axiom, (X1!=X2|~class_OrderedGroup_Oab__group__add(X1)|class_OrderedGroup_Oab__group__add(X2))).
% 1.00/1.63 cnf(i_0_852, axiom, (X1!=X2|~class_OrderedGroup_Opordered__comm__monoid__add(X1)|class_OrderedGroup_Opordered__comm__monoid__add(X2))).
% 1.00/1.63 cnf(i_0_853, axiom, (X1!=X2|~class_Ring__and__Field_Oordered__semidom(X1)|class_Ring__and__Field_Oordered__semidom(X2))).
% 1.00/1.63 cnf(i_0_854, axiom, (X1!=X2|~class_OrderedGroup_Opordered__ab__group__add(X1)|class_OrderedGroup_Opordered__ab__group__add(X2))).
% 1.00/1.63 cnf(i_0_855, axiom, (X1!=X2|~c_Type_Otypings(X1,X3,X4)|c_Type_Otypings(X2,X3,X4))).
% 1.00/1.63 cnf(i_0_856, axiom, (X1!=X2|~c_Type_Otypings(X3,X1,X4)|c_Type_Otypings(X3,X2,X4))).
% 1.00/1.63 cnf(i_0_857, axiom, (X1!=X2|~c_Type_Otypings(X3,X4,X1)|c_Type_Otypings(X3,X4,X2))).
% 1.00/1.63 cnf(i_0_858, axiom, (X1!=X2|~class_OrderedGroup_Olordered__ab__group__add(X1)|class_OrderedGroup_Olordered__ab__group__add(X2))).
% 1.00/1.63 cnf(i_0_859, axiom, (X1!=X2|~class_Ring__and__Field_Oordered__idom(X1)|class_Ring__and__Field_Oordered__idom(X2))).
% 1.00/1.63 cnf(i_0_860, axiom, (X1!=X2|~class_OrderedGroup_Ogroup__add(X1)|class_OrderedGroup_Ogroup__add(X2))).
% 1.00/1.63 cnf(i_0_861, axiom, (X1!=X2|~class_Orderings_Opreorder(X1)|class_Orderings_Opreorder(X2))).
% 1.00/1.63 cnf(i_0_862, axiom, (X1!=X2|~class_Orderings_Oorder(X1)|class_Orderings_Oorder(X2))).
% 1.00/1.63 cnf(i_0_863, axiom, (X1!=X2|~class_Ring__and__Field_Oidom(X1)|class_Ring__and__Field_Oidom(X2))).
% 1.00/1.63 cnf(i_0_864, axiom, (X1!=X2|~class_Int_Onumber__ring(X1)|class_Int_Onumber__ring(X2))).
% 1.00/1.63 cnf(i_0_865, axiom, (X1!=X2|~class_Orderings_Olinorder(X1)|class_Orderings_Olinorder(X2))).
% 1.00/1.63 cnf(i_0_866, axiom, (X1!=X2|~class_OrderedGroup_Ocancel__semigroup__add(X1)|class_OrderedGroup_Ocancel__semigroup__add(X2))).
% 1.00/1.63 cnf(i_0_867, axiom, (X1!=X2|~class_OrderedGroup_Ocancel__ab__semigroup__add(X1)|class_OrderedGroup_Ocancel__ab__semigroup__add(X2))).
% 1.00/1.63 cnf(i_0_868, axiom, (X1!=X2|~hBOOL(X1)|hBOOL(X2))).
% 1.00/1.63 cnf(i_0_869, axiom, (X1!=X2|~c_fequal(X1,X3,X4)|c_fequal(X2,X3,X4))).
% 1.00/1.63 cnf(i_0_870, axiom, (X1!=X2|~c_fequal(X3,X1,X4)|c_fequal(X3,X2,X4))).
% 1.00/1.63 cnf(i_0_871, axiom, (X1!=X2|~c_fequal(X3,X4,X1)|c_fequal(X3,X4,X2))).
% 1.00/1.63 cnf(i_0_872, axiom, (X1!=X2|~class_Nat_Osemiring__char__0(X1)|class_Nat_Osemiring__char__0(X2))).
% 1.00/1.63 cnf(i_0_873, axiom, (X1!=X2|~class_Ring__and__Field_Ozero__neq__one(X1)|class_Ring__and__Field_Ozero__neq__one(X2))).
% 1.00/1.63 cnf(i_0_874, axiom, (X1!=X2|~c_ListOrder_Ostep1(X1,X3,X4,X5)|c_ListOrder_Ostep1(X2,X3,X4,X5))).
% 1.00/1.63 cnf(i_0_875, axiom, (X1!=X2|~c_ListOrder_Ostep1(X3,X1,X4,X5)|c_ListOrder_Ostep1(X3,X2,X4,X5))).
% 1.00/1.63 cnf(i_0_876, axiom, (X1!=X2|~c_ListOrder_Ostep1(X3,X4,X1,X5)|c_ListOrder_Ostep1(X3,X4,X2,X5))).
% 1.00/1.63 cnf(i_0_877, axiom, (X1!=X2|~c_ListOrder_Ostep1(X3,X4,X5,X1)|c_ListOrder_Ostep1(X3,X4,X5,X2))).
% 1.00/1.63 cnf(i_0_878, axiom, (X1!=X2|~c_List_Olistsp(X1,X3,X4)|c_List_Olistsp(X2,X3,X4))).
% 1.00/1.63 cnf(i_0_879, axiom, (X1!=X2|~c_List_Olistsp(X3,X1,X4)|c_List_Olistsp(X3,X2,X4))).
% 1.00/1.63 cnf(i_0_880, axiom, (X1!=X2|~c_List_Olistsp(X3,X4,X1)|c_List_Olistsp(X3,X4,X2))).
% 1.00/1.63 cnf(i_0_881, axiom, (X1!=X2|~c_HOL_Oord__class_Oless(X1,X3,X4)|c_HOL_Oord__class_Oless(X2,X3,X4))).
% 1.00/1.63 cnf(i_0_882, axiom, (X1!=X2|~c_HOL_Oord__class_Oless(X3,X1,X4)|c_HOL_Oord__class_Oless(X3,X2,X4))).
% 1.00/1.63 cnf(i_0_883, axiom, (X1!=X2|~c_HOL_Oord__class_Oless(X3,X4,X1)|c_HOL_Oord__class_Oless(X3,X4,X2))).
% 1.00/1.63 cnf(i_0_884, axiom, (X1!=X2|~class_OrderedGroup_Osemigroup__add(X1)|class_OrderedGroup_Osemigroup__add(X2))).
% 1.00/1.63 cnf(i_0_885, axiom, (X1!=X2|~class_OrderedGroup_Omonoid__add(X1)|class_OrderedGroup_Omonoid__add(X2))).
% 1.00/1.63 cnf(i_0_886, axiom, (X1!=X2|~class_Ring__and__Field_Osemiring__1(X1)|class_Ring__and__Field_Osemiring__1(X2))).
% 2.43/3.12 cnf(i_0_803, axiom, (X1=X1)).
% 2.43/3.12 cnf(i_0_804, axiom, (X1=X2|X2!=X1)).
% 2.43/3.12 cnf(i_0_805, axiom, (X1=X2|X1!=X3|X3!=X2)).
% 2.43/3.12 cnf(i_0_806, axiom, (X1!=X2|hAPP(X1,X3)=hAPP(X2,X3))).
% 2.43/3.12 cnf(i_0_807, axiom, (X1!=X2|hAPP(X3,X1)=hAPP(X3,X2))).
% 2.43/3.12 cnf(i_0_808, axiom, (X1!=X2|c_Type_Oshift(X1,X3,X4,X5)=c_Type_Oshift(X2,X3,X4,X5))).
% 2.43/3.12 cnf(i_0_809, axiom, (X1!=X2|c_Type_Oshift(X3,X1,X4,X5)=c_Type_Oshift(X3,X2,X4,X5))).
% 2.43/3.12 cnf(i_0_810, axiom, (X1!=X2|c_Type_Oshift(X3,X4,X1,X5)=c_Type_Oshift(X3,X4,X2,X5))).
% 2.43/3.12 cnf(i_0_811, axiom, (X1!=X2|c_Type_Oshift(X3,X4,X5,X1)=c_Type_Oshift(X3,X4,X5,X2))).
% 2.43/3.12 cnf(i_0_812, axiom, (X1!=X2|c_Lambda_OdB_OAbs(X1)=c_Lambda_OdB_OAbs(X2))).
% 2.43/3.12 cnf(i_0_813, axiom, (X1!=X2|c_HOL_Ozero__class_Ozero(X1)=c_HOL_Ozero__class_Ozero(X2))).
% 2.43/3.12 cnf(i_0_814, axiom, (X1!=X2|c_HOL_Oone__class_Oone(X1)=c_HOL_Oone__class_Oone(X2))).
% 2.43/3.12 cnf(i_0_815, axiom, (X1!=X2|c_Nat_Osemiring__1__class_Oof__nat(X1,X3)=c_Nat_Osemiring__1__class_Oof__nat(X2,X3))).
% 2.43/3.12 cnf(i_0_816, axiom, (X1!=X2|c_Nat_Osemiring__1__class_Oof__nat(X3,X1)=c_Nat_Osemiring__1__class_Oof__nat(X3,X2))).
% 2.43/3.12 cnf(i_0_817, 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))).
% 2.43/3.12 cnf(i_0_818, 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))).
% 2.43/3.12 cnf(i_0_819, 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))).
% 2.43/3.12 cnf(i_0_820, 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))).
% 2.43/3.12 cnf(i_0_821, axiom, (X1!=X2|c_List_Ofoldl(X1,X3,X4,X5,X6)=c_List_Ofoldl(X2,X3,X4,X5,X6))).
% 2.43/3.12 cnf(i_0_822, axiom, (X1!=X2|c_List_Ofoldl(X3,X1,X4,X5,X6)=c_List_Ofoldl(X3,X2,X4,X5,X6))).
% 2.43/3.12 cnf(i_0_823, axiom, (X1!=X2|c_List_Ofoldl(X3,X4,X1,X5,X6)=c_List_Ofoldl(X3,X4,X2,X5,X6))).
% 2.43/3.12 cnf(i_0_824, axiom, (X1!=X2|c_List_Ofoldl(X3,X4,X5,X1,X6)=c_List_Ofoldl(X3,X4,X5,X2,X6))).
% 2.43/3.12 cnf(i_0_825, axiom, (X1!=X2|c_List_Ofoldl(X3,X4,X5,X6,X1)=c_List_Ofoldl(X3,X4,X5,X6,X2))).
% 2.43/3.12 cnf(i_0_826, axiom, (X1!=X2|c_Lambda_Oliftn(X1,X3,X4)=c_Lambda_Oliftn(X2,X3,X4))).
% 2.43/3.12 cnf(i_0_827, axiom, (X1!=X2|c_Lambda_Oliftn(X3,X1,X4)=c_Lambda_Oliftn(X3,X2,X4))).
% 2.43/3.12 cnf(i_0_828, axiom, (X1!=X2|c_Lambda_Oliftn(X3,X4,X1)=c_Lambda_Oliftn(X3,X4,X2))).
% 2.43/3.12 cnf(i_0_829, axiom, (X1!=X2|c_List_Olist_ONil(X1)=c_List_Olist_ONil(X2))).
% 2.43/3.12 cnf(i_0_830, axiom, (X1!=X2|c_HOL_Ominus__class_Ominus(X1,X3,X4)=c_HOL_Ominus__class_Ominus(X2,X3,X4))).
% 2.43/3.12 cnf(i_0_831, axiom, (X1!=X2|c_HOL_Ominus__class_Ominus(X3,X1,X4)=c_HOL_Ominus__class_Ominus(X3,X2,X4))).
% 2.43/3.12 cnf(i_0_832, axiom, (X1!=X2|c_HOL_Ominus__class_Ominus(X3,X4,X1)=c_HOL_Ominus__class_Ominus(X3,X4,X2))).
% 2.43/3.12 cnf(i_0_833, axiom, (X1!=X2|c_List_Omap(X1,X3,X4,X5)=c_List_Omap(X2,X3,X4,X5))).
% 2.43/3.12 cnf(i_0_834, axiom, (X1!=X2|c_List_Omap(X3,X1,X4,X5)=c_List_Omap(X3,X2,X4,X5))).
% 2.43/3.12 cnf(i_0_835, axiom, (X1!=X2|c_List_Omap(X3,X4,X1,X5)=c_List_Omap(X3,X4,X2,X5))).
% 2.43/3.12 cnf(i_0_836, axiom, (X1!=X2|c_List_Omap(X3,X4,X5,X1)=c_List_Omap(X3,X4,X5,X2))).
% 2.43/3.12 cnf(i_0_837, axiom, (X1!=X2|c_List_Ofoldr(X1,X3,X4,X5,X6)=c_List_Ofoldr(X2,X3,X4,X5,X6))).
% 2.43/3.12 cnf(i_0_838, axiom, (X1!=X2|c_List_Ofoldr(X3,X1,X4,X5,X6)=c_List_Ofoldr(X3,X2,X4,X5,X6))).
% 2.43/3.12 cnf(i_0_839, axiom, (X1!=X2|c_List_Ofoldr(X3,X4,X1,X5,X6)=c_List_Ofoldr(X3,X4,X2,X5,X6))).
% 2.43/3.12 cnf(i_0_840, axiom, (X1!=X2|c_List_Ofoldr(X3,X4,X5,X1,X6)=c_List_Ofoldr(X3,X4,X5,X2,X6))).
% 2.43/3.12 cnf(i_0_841, axiom, (X1!=X2|c_List_Ofoldr(X3,X4,X5,X6,X1)=c_List_Ofoldr(X3,X4,X5,X6,X2))).
% 2.43/3.12 cnf(i_0_842, axiom, (X1!=X2|c_Lambda_OdB_OVar(X1)=c_Lambda_OdB_OVar(X2))).
% 2.43/3.12 cnf(i_0_843, axiom, (X1!=X2|~c_Type_Otyping(X1,X3,X4)|c_Type_Otyping(X2,X3,X4))).
% 2.43/3.12 cnf(i_0_844, axiom, (X1!=X2|~c_Type_Otyping(X3,X1,X4)|c_Type_Otyping(X3,X2,X4))).
% 2.43/3.12 cnf(i_0_845, axiom, (X1!=X2|~c_Type_Otyping(X3,X4,X1)|c_Type_Otyping(X3,X4,X2))).
% 2.43/3.12 cnf(i_0_846, axiom, (X1!=X2|~class_OrderedGroup_Oab__semigroup__add(X1)|class_OrderedGroup_Oab__semigroup__add(X2))).
% 2.43/3.12 cnf(i_0_847, axiom, (X1!=X2|~class_Ring__and__Field_Ocomm__semiring__1(X1)|class_Ring__and__Field_Ocomm__semiring__1(X2))).
% 2.43/3.12 cnf(i_0_848, axiom, (X1!=X2|~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)|class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2))).
% 2.43/3.12 cnf(i_0_849, axiom, (X1!=X2|~class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)|class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2))).
% 2.43/3.12 cnf(i_0_850, axiom, (X1!=X2|~class_OrderedGroup_Ocomm__monoid__add(X1)|class_OrderedGroup_Ocomm__monoid__add(X2))).
% 2.43/3.12 cnf(i_0_851, axiom, (X1!=X2|~class_OrderedGroup_Oab__group__add(X1)|class_OrderedGroup_Oab__group__add(X2))).
% 2.43/3.12 cnf(i_0_852, axiom, (X1!=X2|~class_OrderedGroup_Opordered__comm__monoid__add(X1)|class_OrderedGroup_Opordered__comm__monoid__add(X2))).
% 2.43/3.12 cnf(i_0_853, axiom, (X1!=X2|~class_Ring__and__Field_Oordered__semidom(X1)|class_Ring__and__Field_Oordered__semidom(X2))).
% 2.43/3.12 cnf(i_0_854, axiom, (X1!=X2|~class_OrderedGroup_Opordered__ab__group__add(X1)|class_OrderedGroup_Opordered__ab__group__add(X2))).
% 2.43/3.12 cnf(i_0_855, axiom, (X1!=X2|~c_Type_Otypings(X1,X3,X4)|c_Type_Otypings(X2,X3,X4))).
% 2.43/3.12 cnf(i_0_856, axiom, (X1!=X2|~c_Type_Otypings(X3,X1,X4)|c_Type_Otypings(X3,X2,X4))).
% 2.43/3.12 cnf(i_0_857, axiom, (X1!=X2|~c_Type_Otypings(X3,X4,X1)|c_Type_Otypings(X3,X4,X2))).
% 2.43/3.12 cnf(i_0_858, axiom, (X1!=X2|~class_OrderedGroup_Olordered__ab__group__add(X1)|class_OrderedGroup_Olordered__ab__group__add(X2))).
% 2.43/3.12 cnf(i_0_859, axiom, (X1!=X2|~class_Ring__and__Field_Oordered__idom(X1)|class_Ring__and__Field_Oordered__idom(X2))).
% 2.43/3.12 cnf(i_0_860, axiom, (X1!=X2|~class_OrderedGroup_Ogroup__add(X1)|class_OrderedGroup_Ogroup__add(X2))).
% 2.43/3.12 cnf(i_0_861, axiom, (X1!=X2|~class_Orderings_Opreorder(X1)|class_Orderings_Opreorder(X2))).
% 2.43/3.12 cnf(i_0_862, axiom, (X1!=X2|~class_Orderings_Oorder(X1)|class_Orderings_Oorder(X2))).
% 2.43/3.12 cnf(i_0_863, axiom, (X1!=X2|~class_Ring__and__Field_Oidom(X1)|class_Ring__and__Field_Oidom(X2))).
% 2.43/3.12 cnf(i_0_864, axiom, (X1!=X2|~class_Int_Onumber__ring(X1)|class_Int_Onumber__ring(X2))).
% 2.43/3.12 cnf(i_0_865, axiom, (X1!=X2|~class_Orderings_Olinorder(X1)|class_Orderings_Olinorder(X2))).
% 2.43/3.12 cnf(i_0_866, axiom, (X1!=X2|~class_OrderedGroup_Ocancel__semigroup__add(X1)|class_OrderedGroup_Ocancel__semigroup__add(X2))).
% 2.43/3.12 cnf(i_0_867, axiom, (X1!=X2|~class_OrderedGroup_Ocancel__ab__semigroup__add(X1)|class_OrderedGroup_Ocancel__ab__semigroup__add(X2))).
% 2.43/3.12 cnf(i_0_868, axiom, (X1!=X2|~hBOOL(X1)|hBOOL(X2))).
% 2.43/3.12 cnf(i_0_869, axiom, (X1!=X2|~c_fequal(X1,X3,X4)|c_fequal(X2,X3,X4))).
% 2.43/3.12 cnf(i_0_870, axiom, (X1!=X2|~c_fequal(X3,X1,X4)|c_fequal(X3,X2,X4))).
% 2.43/3.12 cnf(i_0_871, axiom, (X1!=X2|~c_fequal(X3,X4,X1)|c_fequal(X3,X4,X2))).
% 2.43/3.12 cnf(i_0_872, axiom, (X1!=X2|~class_Nat_Osemiring__char__0(X1)|class_Nat_Osemiring__char__0(X2))).
% 2.43/3.12 cnf(i_0_873, axiom, (X1!=X2|~class_Ring__and__Field_Ozero__neq__one(X1)|class_Ring__and__Field_Ozero__neq__one(X2))).
% 2.43/3.12 cnf(i_0_874, axiom, (X1!=X2|~c_ListOrder_Ostep1(X1,X3,X4,X5)|c_ListOrder_Ostep1(X2,X3,X4,X5))).
% 2.43/3.12 cnf(i_0_875, axiom, (X1!=X2|~c_ListOrder_Ostep1(X3,X1,X4,X5)|c_ListOrder_Ostep1(X3,X2,X4,X5))).
% 2.43/3.12 cnf(i_0_876, axiom, (X1!=X2|~c_ListOrder_Ostep1(X3,X4,X1,X5)|c_ListOrder_Ostep1(X3,X4,X2,X5))).
% 2.43/3.12 cnf(i_0_877, axiom, (X1!=X2|~c_ListOrder_Ostep1(X3,X4,X5,X1)|c_ListOrder_Ostep1(X3,X4,X5,X2))).
% 2.43/3.12 cnf(i_0_878, axiom, (X1!=X2|~c_List_Olistsp(X1,X3,X4)|c_List_Olistsp(X2,X3,X4))).
% 2.43/3.12 cnf(i_0_879, axiom, (X1!=X2|~c_List_Olistsp(X3,X1,X4)|c_List_Olistsp(X3,X2,X4))).
% 2.43/3.12 cnf(i_0_880, axiom, (X1!=X2|~c_List_Olistsp(X3,X4,X1)|c_List_Olistsp(X3,X4,X2))).
% 2.43/3.12 cnf(i_0_881, axiom, (X1!=X2|~c_HOL_Oord__class_Oless(X1,X3,X4)|c_HOL_Oord__class_Oless(X2,X3,X4))).
% 2.43/3.12 cnf(i_0_882, axiom, (X1!=X2|~c_HOL_Oord__class_Oless(X3,X1,X4)|c_HOL_Oord__class_Oless(X3,X2,X4))).
% 2.43/3.12 cnf(i_0_883, axiom, (X1!=X2|~c_HOL_Oord__class_Oless(X3,X4,X1)|c_HOL_Oord__class_Oless(X3,X4,X2))).
% 2.43/3.12 cnf(i_0_884, axiom, (X1!=X2|~class_OrderedGroup_Osemigroup__add(X1)|class_OrderedGroup_Osemigroup__add(X2))).
% 2.43/3.12 cnf(i_0_885, axiom, (X1!=X2|~class_OrderedGroup_Omonoid__add(X1)|class_OrderedGroup_Omonoid__add(X2))).
% 2.43/3.12 cnf(i_0_886, axiom, (X1!=X2|~class_Ring__and__Field_Osemiring__1(X1)|class_Ring__and__Field_Osemiring__1(X2))).
% 2.43/3.12 cnf(i_0_887, plain, (X1=X1), inference(equality_inference,[],[460])).
% 2.43/3.12 cnf(i_0_888, plain, (X1=X1), inference(equality_inference,[],[461])).
% 2.43/3.12 cnf(i_0_889, plain, (X1=X1), inference(equality_inference,[],[462])).
% 2.43/3.12 cnf(i_0_890, plain, (X1=X1), inference(equality_inference,[],[463])).
% 2.43/3.12 cnf(i_0_891, plain, (X1=X1), inference(equality_inference,[],[466])).
% 2.43/3.12 cnf(i_0_892, 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,[],[555])).
% 2.43/3.12 cnf(i_0_893, 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,[],[608])).
% 2.43/3.12 cnf(i_0_894, 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,[],[609])).
% 2.43/3.12 cnf(i_0_895, 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,[],[638])).
% 2.43/3.12 cnf(i_0_896, 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,[],[639])).
% 2.43/3.12 cnf(i_0_897, 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,[],[640])).
% 2.43/3.12 cnf(i_0_898, 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,[],[641])).
% 2.43/3.12 cnf(i_0_899, plain, (~class_Int_Onumber__ring(X1)|X2=X2|~class_Ring__and__Field_Oidom(X1)), inference(equality_inference,[],[657])).
% 2.43/3.12 cnf(i_0_900, plain, (X1=X1|~class_OrderedGroup_Oab__group__add(X2)), inference(equality_inference,[],[658])).
% 2.43/3.12 cnf(i_0_901, plain, (X1=X1|~class_OrderedGroup_Oab__group__add(X2)), inference(equality_inference,[],[659])).
% 2.43/3.12 cnf(i_0_902, plain, (X1=X1|~class_OrderedGroup_Ocancel__semigroup__add(X2)), inference(equality_inference,[],[666])).
% 2.43/3.12 cnf(i_0_903, plain, (X1=X1|~class_OrderedGroup_Ocancel__semigroup__add(X2)), inference(equality_inference,[],[667])).
% 2.43/3.12 cnf(i_0_904, plain, (X1=X1|~class_OrderedGroup_Ocancel__ab__semigroup__add(X2)), inference(equality_inference,[],[668])).
% 2.43/3.12 cnf(i_0_905, 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,[],[670])).
% 2.43/3.12 cnf(i_0_906, 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,[],[671])).
% 2.43/3.12 cnf(i_0_907, plain, (X1=X1), inference(equality_inference,[],[684])).
% 2.43/3.12 cnf(i_0_908, plain, (X1=X1), inference(equality_inference,[],[686])).
% 2.43/3.12 cnf(i_0_909, plain, (X1=X1), inference(equality_inference,[],[697])).
% 2.43/3.12 cnf(i_0_910, plain, (X1=X1), inference(equality_inference,[],[698])).
% 2.43/3.12 cnf(i_0_911, plain, (X1=X1), inference(equality_inference,[],[699])).
% 2.43/3.12 cnf(i_0_912, plain, (X1=X1), inference(equality_inference,[],[700])).
% 2.43/3.12 cnf(i_0_913, plain, (X1=X1|~class_Nat_Osemiring__char__0(X2)), inference(equality_inference,[],[765])).
% 2.43/3.12 cnf(i_0_914, plain, (X1=X1), inference(equality_inference,[],[780])).
% 2.43/3.12 cnf(i_0_915, plain, (X1=X1), inference(equality_inference,[],[781])).
% 2.43/3.12 cnf(i_0_916, plain, (~c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,X1)), inference(scs_inference,[],[i_0_801,i_0_506])).
% 2.43/3.12 cnf(i_0_917, plain, (c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,c_Type_Osko__Type__Xvar__app__typesE__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_n____,v_rs____))), inference(scs_inference,[],[i_0_470,i_0_456])).
% 2.43/3.12 cnf(i_0_918, plain, (~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)|c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3))), inference(rename_variables,[],[i_0_456])).
% 2.43/3.12 cnf(i_0_919, plain, (c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_rs____))), inference(scs_inference,[],[i_0_470,i_0_456,i_0_457])).
% 2.43/3.12 cnf(i_0_920, plain, (~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)|c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeD__1__1(X4,X1,X2,X3))), inference(rename_variables,[],[i_0_457])).
% 2.43/3.12 cnf(i_0_921, plain, (c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_rs____,c_Type_Osko__Type__Xlist__app__typeE__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_rs____))), inference(scs_inference,[],[i_0_470,i_0_456,i_0_457,i_0_458])).
% 2.43/3.12 cnf(i_0_922, plain, (~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)|c_Type_Otypings(X1,X3,c_Type_Osko__Type__Xlist__app__typeE__1__1(X4,X1,X2,X3))), inference(rename_variables,[],[i_0_458])).
% 2.43/3.12 cnf(i_0_923, plain, (c_List_Ofoldl(c_Lambda_OdB_OApp,X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_List_Olist_ONil(tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)),tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(X2)), inference(scs_inference,[],[i_0_470,i_0_734,i_0_456,i_0_457,i_0_458,i_0_485])).
% 2.43/3.12 cnf(i_0_924, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))!=X1), inference(rename_variables,[],[i_0_734])).
% 2.43/3.12 cnf(i_0_925, plain, (X1=c_List_Olist_ONil(tc_Lambda_OdB)|c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X1,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(X3)), inference(rename_variables,[],[i_0_485])).
% 2.43/3.12 cnf(i_0_926, plain, (c_Lambda_OdB_OVar(X1)!=c_List_Ofoldl(c_Lambda_OdB_OApp,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_List_Olist_ONil(tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)),tc_Lambda_OdB,tc_Lambda_OdB)), inference(scs_inference,[],[i_0_470,i_0_734,i_0_924,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486])).
% 2.43/3.12 cnf(i_0_927, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))!=X1), inference(rename_variables,[],[i_0_734])).
% 2.43/3.12 cnf(i_0_928, plain, (X1=c_List_Olist_ONil(tc_Lambda_OdB)|c_Lambda_OdB_OVar(X2)!=c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)), inference(rename_variables,[],[i_0_486])).
% 2.43/3.12 cnf(i_0_929, plain, (c_Lambda_OdB_OAbs(X1)!=c_List_Ofoldl(c_Lambda_OdB_OApp,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_List_Olist_ONil(tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)),tc_Lambda_OdB,tc_Lambda_OdB)), inference(scs_inference,[],[i_0_470,i_0_734,i_0_924,i_0_927,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487])).
% 2.43/3.12 cnf(i_0_930, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))!=X1), inference(rename_variables,[],[i_0_734])).
% 2.43/3.12 cnf(i_0_931, plain, (X1=c_List_Olist_ONil(tc_Lambda_OdB)|c_Lambda_OdB_OAbs(X2)!=c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)), inference(rename_variables,[],[i_0_487])).
% 2.43/3.12 cnf(i_0_932, plain, (~class_OrderedGroup_Ogroup__add(tc_nat)), inference(scs_inference,[],[i_0_470,i_0_734,i_0_924,i_0_927,i_0_729,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607])).
% 2.43/3.12 cnf(i_0_933, 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(rename_variables,[],[i_0_729])).
% 2.43/3.12 cnf(i_0_934, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3)=X2|~class_OrderedGroup_Ogroup__add(X1)), inference(rename_variables,[],[i_0_607])).
% 2.43/3.12 cnf(i_0_935, plain, (~c_Type_Otyping(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2),c_Lambda_OdB_OVar(X3))), inference(scs_inference,[],[i_0_470,i_0_752,i_0_734,i_0_924,i_0_927,i_0_729,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706])).
% 2.43/3.12 cnf(i_0_936, plain, (hAPP(X1,X2)=X3|~c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),X3)), inference(rename_variables,[],[i_0_706])).
% 2.43/3.12 cnf(i_0_937, plain, (~c_fequal(c_Lambda_OdB_OVar(X1),c_Lambda_OdB_OAbs(X2),X3)), inference(scs_inference,[],[i_0_470,i_0_782,i_0_752,i_0_734,i_0_924,i_0_927,i_0_729,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722])).
% 2.43/3.12 cnf(i_0_938, plain, (X1=X2|~c_fequal(X1,X2,X3)), inference(rename_variables,[],[i_0_722])).
% 2.43/3.12 cnf(i_0_939, plain, (c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(X1,X1,tc_nat)), inference(scs_inference,[],[i_0_763,i_0_470,i_0_782,i_0_752,i_0_734,i_0_924,i_0_927,i_0_729,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804])).
% 2.43/3.12 cnf(i_0_940, plain, (hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(X1,c_HOL_Oone__class_Oone(tc_nat)))!=X1), inference(scs_inference,[],[i_0_763,i_0_470,i_0_782,i_0_752,i_0_734,i_0_924,i_0_927,i_0_930,i_0_729,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806])).
% 2.43/3.12 cnf(i_0_941, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))!=X1), inference(rename_variables,[],[i_0_734])).
% 2.43/3.12 cnf(i_0_942, plain, (c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_n____,v_rs____),v_T_H____,tc_Type_Otype,tc_Type_Otype))), inference(scs_inference,[],[i_0_763,i_0_470,i_0_782,i_0_752,i_0_734,i_0_924,i_0_927,i_0_930,i_0_729,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449])).
% 2.43/3.12 cnf(i_0_943, plain, (~c_Type_Otyping(X1,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)|c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X4,X1,X2,X3),X4,tc_Type_Otype,tc_Type_Otype))), inference(rename_variables,[],[i_0_449])).
% 2.43/3.12 cnf(i_0_944, plain, (c_Type_Otyping(X1,c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X2)),hAPP(hAPP(c_Type_Otype_OFun,X3),hAPP(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_Type_Otype),X2)))), inference(scs_inference,[],[i_0_763,i_0_470,i_0_723,i_0_782,i_0_752,i_0_734,i_0_924,i_0_927,i_0_930,i_0_729,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501])).
% 2.43/3.12 cnf(i_0_945, plain, (c_Type_Otyping(X1,c_Lambda_OdB_OVar(X2),hAPP(X1,X2))), inference(rename_variables,[],[i_0_723])).
% 2.43/3.12 cnf(i_0_946, plain, (~c_Type_Otyping(c_Type_Oshift(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X3,X4)|c_Type_Otyping(X1,c_Lambda_OdB_OAbs(X3),hAPP(hAPP(c_Type_Otype_OFun,X2),X4))), inference(rename_variables,[],[i_0_501])).
% 2.43/3.12 cnf(i_0_947, 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),c_HOL_Oone__class_Oone(tc_nat))),X2),tc_nat)), inference(scs_inference,[],[i_0_763,i_0_470,i_0_723,i_0_782,i_0_752,i_0_524,i_0_734,i_0_924,i_0_927,i_0_930,i_0_729,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534])).
% 2.43/3.12 cnf(i_0_948, 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(rename_variables,[],[i_0_524])).
% 2.43/3.12 cnf(i_0_949, 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(rename_variables,[],[i_0_534])).
% 2.43/3.12 cnf(i_0_950, plain, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat),tc_nat)), inference(scs_inference,[],[i_0_763,i_0_470,i_0_725,i_0_723,i_0_782,i_0_752,i_0_524,i_0_734,i_0_924,i_0_927,i_0_930,i_0_729,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554])).
% 2.43/3.12 cnf(i_0_951, plain, (~c_HOL_Oord__class_Oless(X1,X1,tc_nat)), inference(rename_variables,[],[i_0_725])).
% 2.43/3.12 cnf(i_0_952, plain, (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)), inference(rename_variables,[],[i_0_554])).
% 2.43/3.12 cnf(i_0_953, plain, (c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(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)),X2,tc_nat),tc_nat)), inference(scs_inference,[],[i_0_763,i_0_470,i_0_725,i_0_723,i_0_782,i_0_752,i_0_682,i_0_524,i_0_734,i_0_924,i_0_927,i_0_930,i_0_729,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556])).
% 2.43/3.12 cnf(i_0_954, 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(rename_variables,[],[i_0_682])).
% 2.43/3.12 cnf(i_0_955, plain, (~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)), inference(rename_variables,[],[i_0_556])).
% 2.43/3.12 cnf(i_0_956, plain, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)), inference(scs_inference,[],[i_0_763,i_0_470,i_0_725,i_0_723,i_0_782,i_0_752,i_0_682,i_0_524,i_0_734,i_0_924,i_0_927,i_0_930,i_0_620,i_0_729,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583])).
% 2.43/3.12 cnf(i_0_957, 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(X2,X1,tc_nat)), inference(rename_variables,[],[i_0_583])).
% 2.43/3.12 cnf(i_0_958, 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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3))),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)), inference(scs_inference,[],[i_0_763,i_0_470,i_0_725,i_0_723,i_0_782,i_0_752,i_0_682,i_0_524,i_0_525,i_0_734,i_0_924,i_0_927,i_0_930,i_0_620,i_0_729,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606])).
% 2.43/3.12 cnf(i_0_959, 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(rename_variables,[],[i_0_525])).
% 2.43/3.12 cnf(i_0_960, plain, (~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,X3,tc_nat)), inference(rename_variables,[],[i_0_606])).
% 2.43/3.12 cnf(i_0_961, plain, (~c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1),tc_nat)), inference(scs_inference,[],[i_0_763,i_0_470,i_0_725,i_0_723,i_0_782,i_0_752,i_0_682,i_0_524,i_0_525,i_0_734,i_0_924,i_0_927,i_0_930,i_0_620,i_0_729,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621])).
% 2.43/3.12 cnf(i_0_962, plain, (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)), inference(rename_variables,[],[i_0_621])).
% 2.43/3.12 cnf(i_0_963, plain, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),tc_nat)), inference(scs_inference,[],[i_0_763,i_0_470,i_0_725,i_0_723,i_0_782,i_0_752,i_0_682,i_0_524,i_0_525,i_0_734,i_0_924,i_0_927,i_0_930,i_0_620,i_0_729,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623])).
% 2.43/3.12 cnf(i_0_964, plain, (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)), inference(rename_variables,[],[i_0_623])).
% 2.43/3.12 cnf(i_0_965, plain, (hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2))),c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),X2),c_HOL_Ozero__class_Ozero(tc_nat)))))), inference(scs_inference,[],[i_0_763,i_0_470,i_0_725,i_0_723,i_0_782,i_0_752,i_0_682,i_0_524,i_0_525,i_0_734,i_0_924,i_0_927,i_0_930,i_0_620,i_0_729,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630])).
% 2.43/3.12 cnf(i_0_966, plain, (~hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))|hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1)),c_Lambda_OdB_OAbs(X2)))), inference(rename_variables,[],[i_0_630])).
% 2.43/3.12 cnf(i_0_967, plain, (~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3),X1,tc_nat)), inference(scs_inference,[],[i_0_763,i_0_470,i_0_725,i_0_723,i_0_782,i_0_752,i_0_682,i_0_524,i_0_525,i_0_734,i_0_924,i_0_927,i_0_930,i_0_620,i_0_729,i_0_636,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633])).
% 2.43/3.12 cnf(i_0_968, plain, (~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat)), inference(rename_variables,[],[i_0_636])).
% 2.43/3.12 cnf(i_0_969, plain, (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)), inference(rename_variables,[],[i_0_633])).
% 2.43/3.12 cnf(i_0_970, plain, (~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3),X2,tc_nat)), inference(scs_inference,[],[i_0_763,i_0_470,i_0_725,i_0_723,i_0_782,i_0_752,i_0_682,i_0_524,i_0_525,i_0_734,i_0_924,i_0_927,i_0_930,i_0_620,i_0_729,i_0_636,i_0_968,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635])).
% 2.43/3.12 cnf(i_0_971, plain, (~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X1,tc_nat)), inference(rename_variables,[],[i_0_636])).
% 2.43/3.12 cnf(i_0_972, plain, (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)), inference(rename_variables,[],[i_0_635])).
% 2.43/3.12 cnf(i_0_973, plain, (c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))),tc_nat)), inference(scs_inference,[],[i_0_763,i_0_470,i_0_725,i_0_723,i_0_782,i_0_752,i_0_682,i_0_524,i_0_525,i_0_734,i_0_924,i_0_927,i_0_930,i_0_620,i_0_729,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651])).
% 2.43/3.12 cnf(i_0_974, plain, (~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat)), inference(rename_variables,[],[i_0_637])).
% 2.43/3.12 cnf(i_0_975, 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(X2,X1,tc_nat)), inference(rename_variables,[],[i_0_651])).
% 2.43/3.12 cnf(i_0_976, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1)), inference(scs_inference,[],[i_0_763,i_0_470,i_0_725,i_0_723,i_0_782,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_620,i_0_729,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599])).
% 2.43/3.12 cnf(i_0_977, 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(rename_variables,[],[i_0_525])).
% 2.43/3.12 cnf(i_0_978, 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)|X1=X2), inference(rename_variables,[],[i_0_599])).
% 2.43/3.12 cnf(i_0_979, plain, (~class_OrderedGroup_Oab__group__add(tc_nat)), inference(scs_inference,[],[i_0_763,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658])).
% 2.43/3.12 cnf(i_0_980, 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(rename_variables,[],[i_0_592])).
% 2.43/3.12 cnf(i_0_981, 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(rename_variables,[],[i_0_731])).
% 2.43/3.12 cnf(i_0_982, plain, (c_HOL_Ominus__class_Ominus(X1,X2,X3)!=c_HOL_Ominus__class_Ominus(X4,X4,X3)|X1=X2|~class_OrderedGroup_Oab__group__add(X3)), inference(rename_variables,[],[i_0_658])).
% 2.43/3.12 cnf(i_0_983, plain, (c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1),X1,tc_nat)), inference(scs_inference,[],[i_0_763,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708])).
% 2.43/3.12 cnf(i_0_984, plain, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)), inference(rename_variables,[],[i_0_721])).
% 2.43/3.12 cnf(i_0_985, plain, (c_HOL_Oord__class_Oless(X1,X2,tc_nat)|c_HOL_Oord__class_Oless(X2,X1,tc_nat)|X1=X2), inference(rename_variables,[],[i_0_708])).
% 2.43/3.12 cnf(i_0_986, 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_Oone__class_Oone(tc_nat))!=c_HOL_Oone__class_Oone(tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805])).
% 2.43/3.12 cnf(i_0_987, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))!=X1), inference(rename_variables,[],[i_0_734])).
% 2.43/3.12 cnf(i_0_988, plain, (~c_Type_Otyping(c_List_Ofoldr(X1,c_List_Olist_ONil(X2),hAPP(c_Lambda_OdB_OApp,X3),X2,X4),c_Lambda_OdB_OVar(X5),c_Lambda_OdB_OVar(X6))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843])).
% 2.43/3.12 cnf(i_0_989, plain, (c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4)=X3), inference(rename_variables,[],[i_0_497])).
% 2.43/3.12 cnf(i_0_990, plain, (~c_Type_Otyping(hAPP(c_Lambda_OdB_OApp,X1),c_List_Ofoldr(X2,c_List_Olist_ONil(X3),c_Lambda_OdB_OVar(X4),X3,X5),c_Lambda_OdB_OVar(X6))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844])).
% 2.43/3.12 cnf(i_0_991, plain, (c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4)=X3), inference(rename_variables,[],[i_0_497])).
% 2.43/3.12 cnf(i_0_992, plain, (~c_Type_Otyping(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X2),c_List_Ofoldr(X3,c_List_Olist_ONil(X4),c_Lambda_OdB_OVar(X5),X4,X6))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845])).
% 2.43/3.12 cnf(i_0_993, plain, (c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4)=X3), inference(rename_variables,[],[i_0_497])).
% 2.43/3.12 cnf(i_0_994, plain, (class_Ring__and__Field_Osemiring__1(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_768,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886])).
% 2.43/3.12 cnf(i_0_995, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_996, plain, (class_OrderedGroup_Oab__semigroup__add(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_768,i_0_995,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_793,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846])).
% 2.43/3.12 cnf(i_0_997, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_998, plain, (class_Ring__and__Field_Ocomm__semiring__1(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_768,i_0_995,i_0_997,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_790,i_0_793,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847])).
% 2.43/3.12 cnf(i_0_999, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1000, plain, (class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_768,i_0_995,i_0_997,i_0_999,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_790,i_0_793,i_0_794,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848])).
% 2.43/3.12 cnf(i_0_1001, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1002, plain, (class_OrderedGroup_Opordered__cancel__ab__semigroup__add(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_790,i_0_793,i_0_794,i_0_796,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849])).
% 2.43/3.12 cnf(i_0_1003, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1004, plain, (class_OrderedGroup_Ocomm__monoid__add(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_789,i_0_790,i_0_793,i_0_794,i_0_796,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850])).
% 2.43/3.12 cnf(i_0_1005, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1006, plain, (class_OrderedGroup_Opordered__comm__monoid__add(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_789,i_0_790,i_0_793,i_0_794,i_0_796,i_0_797,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852])).
% 2.43/3.12 cnf(i_0_1007, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1008, plain, (class_Ring__and__Field_Oordered__semidom(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_789,i_0_790,i_0_793,i_0_794,i_0_796,i_0_797,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853])).
% 2.43/3.12 cnf(i_0_1009, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1010, plain, (class_Orderings_Opreorder(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_785,i_0_789,i_0_790,i_0_793,i_0_794,i_0_796,i_0_797,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861])).
% 2.43/3.12 cnf(i_0_1011, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1012, plain, (class_Orderings_Oorder(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_785,i_0_786,i_0_789,i_0_790,i_0_793,i_0_794,i_0_796,i_0_797,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862])).
% 2.43/3.12 cnf(i_0_1013, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1014, plain, (class_Orderings_Olinorder(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_784,i_0_785,i_0_786,i_0_789,i_0_790,i_0_793,i_0_794,i_0_796,i_0_797,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865])).
% 2.43/3.12 cnf(i_0_1015, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1016, plain, (class_OrderedGroup_Ocancel__semigroup__add(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_784,i_0_785,i_0_786,i_0_787,i_0_789,i_0_790,i_0_793,i_0_794,i_0_796,i_0_797,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866])).
% 2.43/3.12 cnf(i_0_1017, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1018, plain, (class_OrderedGroup_Ocancel__ab__semigroup__add(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_793,i_0_794,i_0_796,i_0_797,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867])).
% 2.43/3.12 cnf(i_0_1019, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1020, plain, (hAPP(c_InductTermi_OIT,v_u____)!=hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X1)),X2)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_793,i_0_794,i_0_796,i_0_797,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868])).
% 2.43/3.12 cnf(i_0_1021, plain, (~c_fequal(c_List_Ofoldr(X1,c_List_Olist_ONil(X2),c_Lambda_OdB_OVar(X3),X2,X4),c_Lambda_OdB_OAbs(X5),X6)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_993,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_793,i_0_794,i_0_796,i_0_797,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869])).
% 2.43/3.12 cnf(i_0_1022, plain, (c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4)=X3), inference(rename_variables,[],[i_0_497])).
% 2.43/3.12 cnf(i_0_1023, plain, (~c_fequal(c_Lambda_OdB_OVar(X1),c_List_Ofoldr(X2,c_List_Olist_ONil(X3),c_Lambda_OdB_OAbs(X4),X3,X5),X6)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_793,i_0_794,i_0_796,i_0_797,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870])).
% 2.43/3.12 cnf(i_0_1024, plain, (c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4)=X3), inference(rename_variables,[],[i_0_497])).
% 2.43/3.12 cnf(i_0_1025, plain, (class_Nat_Osemiring__char__0(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_792,i_0_793,i_0_794,i_0_796,i_0_797,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872])).
% 2.43/3.12 cnf(i_0_1026, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1027, plain, (class_Ring__and__Field_Ozero__neq__one(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_470,i_0_592,i_0_725,i_0_723,i_0_782,i_0_721,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_792,i_0_793,i_0_794,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873])).
% 2.43/3.12 cnf(i_0_1028, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1029, plain, (~c_ListOrder_Ostep1(X1,c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X4),X5,X4)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_470,i_0_592,i_0_551,i_0_725,i_0_723,i_0_782,i_0_721,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_792,i_0_793,i_0_794,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875])).
% 2.43/3.12 cnf(i_0_1030, plain, (~c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2)), inference(rename_variables,[],[i_0_551])).
% 2.43/3.12 cnf(i_0_1031, plain, (~c_ListOrder_Ostep1(X1,X2,c_List_Omap(X3,c_List_Olist_ONil(X4),X4,X5),X5)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_470,i_0_592,i_0_551,i_0_552,i_0_725,i_0_723,i_0_782,i_0_721,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_792,i_0_793,i_0_794,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876])).
% 2.43/3.12 cnf(i_0_1032, plain, (~c_ListOrder_Ostep1(X1,X2,c_List_Olist_ONil(X3),X3)), inference(rename_variables,[],[i_0_552])).
% 2.43/3.12 cnf(i_0_1033, plain, (~c_ListOrder_Ostep1(X1,c_List_Olist_ONil(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),X2,c_HOL_Oone__class_Oone(tc_nat))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_470,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_723,i_0_782,i_0_721,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_792,i_0_793,i_0_794,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877])).
% 2.43/3.12 cnf(i_0_1034, plain, (~c_ListOrder_Ostep1(X1,c_List_Olist_ONil(X2),X3,X2)), inference(rename_variables,[],[i_0_551])).
% 2.43/3.12 cnf(i_0_1035, plain, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X2,tc_nat),tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_470,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_792,i_0_793,i_0_794,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882])).
% 2.43/3.12 cnf(i_0_1036, plain, (~c_HOL_Oord__class_Oless(X1,X1,c_List_Ofoldr(X2,c_List_Olist_ONil(X3),tc_nat,X3,X4))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_470,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_792,i_0_793,i_0_794,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883])).
% 2.43/3.12 cnf(i_0_1037, plain, (c_List_Ofoldr(X1,c_List_Olist_ONil(X2),X3,X2,X4)=X3), inference(rename_variables,[],[i_0_497])).
% 2.43/3.12 cnf(i_0_1038, plain, (class_OrderedGroup_Osemigroup__add(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_470,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884])).
% 2.43/3.12 cnf(i_0_1039, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1040, plain, (class_OrderedGroup_Omonoid__add(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885])).
% 2.43/3.12 cnf(i_0_1041, plain, (X1=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))), inference(rename_variables,[],[i_0_768])).
% 2.43/3.12 cnf(i_0_1042, plain, (c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),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))),X3)),tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529])).
% 2.43/3.12 cnf(i_0_1043, plain, (~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)), inference(rename_variables,[],[i_0_529])).
% 2.43/3.12 cnf(i_0_1044, plain, (c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X1))),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),hAPP(c_Type_Oshift(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat),v_T_H____,tc_Type_Otype),X1))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546])).
% 2.43/3.12 cnf(i_0_1045, plain, (~c_Type_Otyping(X1,X2,hAPP(hAPP(c_Type_Otype_OFun,X3),X4))|c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X5),X4)|~c_Type_Otyping(X1,X5,X3)), inference(rename_variables,[],[i_0_546])).
% 2.43/3.12 cnf(i_0_1046, plain, (~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)))),X2,tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547])).
% 2.43/3.12 cnf(i_0_1047, plain, (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)), inference(rename_variables,[],[i_0_547])).
% 2.43/3.12 cnf(i_0_1048, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571])).
% 2.43/3.12 cnf(i_0_1049, 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(rename_variables,[],[i_0_682])).
% 2.43/3.12 cnf(i_0_1050, plain, (~c_HOL_Oord__class_Oless(X1,X1,tc_nat)), inference(rename_variables,[],[i_0_725])).
% 2.43/3.12 cnf(i_0_1051, plain, (~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)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)), inference(rename_variables,[],[i_0_571])).
% 2.43/3.12 cnf(i_0_1052, plain, (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(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)),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(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572])).
% 2.43/3.12 cnf(i_0_1053, 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(rename_variables,[],[i_0_682])).
% 2.43/3.12 cnf(i_0_1054, plain, (~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_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat)), inference(rename_variables,[],[i_0_572])).
% 2.43/3.12 cnf(i_0_1055, plain, (~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605])).
% 2.43/3.12 cnf(i_0_1056, 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(rename_variables,[],[i_0_559])).
% 2.43/3.12 cnf(i_0_1057, plain, (~c_HOL_Oord__class_Oless(X1,X1,tc_nat)), inference(rename_variables,[],[i_0_725])).
% 2.43/3.12 cnf(i_0_1058, plain, (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)|c_HOL_Oord__class_Oless(X1,X4,tc_nat)), inference(rename_variables,[],[i_0_605])).
% 2.43/3.12 cnf(i_0_1059, plain, (~class_OrderedGroup_Opordered__ab__group__add(tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614])).
% 2.43/3.12 cnf(i_0_1060, plain, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)), inference(rename_variables,[],[i_0_721])).
% 2.43/3.12 cnf(i_0_1061, plain, (c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)|~class_OrderedGroup_Opordered__ab__group__add(X3)|~c_HOL_Oord__class_Oless(X1,X2,X3)), inference(rename_variables,[],[i_0_614])).
% 2.43/3.12 cnf(i_0_1062, plain, (~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652])).
% 2.43/3.12 cnf(i_0_1063, plain, (~c_HOL_Oord__class_Oless(X1,X1,tc_nat)), inference(rename_variables,[],[i_0_725])).
% 2.43/3.12 cnf(i_0_1064, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)|~class_Ring__and__Field_Oordered__semidom(X2)), inference(rename_variables,[],[i_0_652])).
% 2.43/3.12 cnf(i_0_1065, plain, (c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652,i_0_654])).
% 2.43/3.12 cnf(i_0_1066, plain, (~c_HOL_Oord__class_Oless(X1,X2,tc_nat)|c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)|~class_Ring__and__Field_Oordered__semidom(X3)), inference(rename_variables,[],[i_0_654])).
% 2.43/3.12 cnf(i_0_1067, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__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),tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652,i_0_654,i_0_656])).
% 2.43/3.12 cnf(i_0_1068, 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(rename_variables,[],[i_0_682])).
% 2.43/3.12 cnf(i_0_1069, plain, (~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)|~class_Ring__and__Field_Oordered__semidom(X2)), inference(rename_variables,[],[i_0_656])).
% 2.43/3.12 cnf(i_0_1070, plain, (~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652,i_0_654,i_0_656,i_0_660])).
% 2.43/3.12 cnf(i_0_1071, 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(rename_variables,[],[i_0_620])).
% 2.43/3.12 cnf(i_0_1072, plain, (~c_HOL_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Olinorder(X3)|~c_HOL_Oord__class_Oless(X2,X1,X3)), inference(rename_variables,[],[i_0_660])).
% 2.43/3.12 cnf(i_0_1073, plain, (~c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_1071,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652,i_0_654,i_0_656,i_0_660,i_0_662])).
% 2.43/3.12 cnf(i_0_1074, plain, (~c_HOL_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Opreorder(X3)|~c_HOL_Oord__class_Oless(X2,X1,X3)), inference(rename_variables,[],[i_0_662])).
% 2.43/3.12 cnf(i_0_1075, plain, (~c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(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)),X2,tc_nat),X1,tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_1071,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652,i_0_654,i_0_656,i_0_660,i_0_662,i_0_663])).
% 2.43/3.12 cnf(i_0_1076, plain, (~c_HOL_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Oorder(X3)|~c_HOL_Oord__class_Oless(X2,X1,X3)), inference(rename_variables,[],[i_0_663])).
% 2.43/3.12 cnf(i_0_1077, plain, (~c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2),X2,tc_nat),tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_1071,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652,i_0_654,i_0_656,i_0_660,i_0_662,i_0_663,i_0_881])).
% 2.43/3.12 cnf(i_0_1078, plain, (c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1),X1,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1),X1,tc_nat),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1),X1,tc_nat),tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_1071,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652,i_0_654,i_0_656,i_0_660,i_0_662,i_0_663,i_0_881,i_0_695])).
% 2.43/3.12 cnf(i_0_1079, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|~class_Orderings_Olinorder(X3)|X1=X2|c_HOL_Oord__class_Oless(X2,X1,X3)), inference(rename_variables,[],[i_0_695])).
% 2.43/3.12 cnf(i_0_1080, plain, (c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),c_Type_Osko__Type__Xtyping__elims__2__1(hAPP(c_Type_Oshift(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat),v_T_H____,tc_Type_Otype),X1),c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X1)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_1071,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652,i_0_654,i_0_656,i_0_660,i_0_662,i_0_663,i_0_881,i_0_695,i_0_510])).
% 2.43/3.12 cnf(i_0_1081, plain, (~c_Type_Otyping(X1,hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3),X4)|c_Type_Otyping(X1,X3,c_Type_Osko__Type__Xtyping__elims__2__1(X4,X1,X2,X3))), inference(rename_variables,[],[i_0_510])).
% 2.43/3.12 cnf(i_0_1082, plain, (c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_1071,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652,i_0_654,i_0_656,i_0_660,i_0_662,i_0_663,i_0_881,i_0_695,i_0_510,i_0_757])).
% 2.43/3.12 cnf(i_0_1083, plain, (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)|X1=c_HOL_Ozero__class_Ozero(tc_nat)), inference(rename_variables,[],[i_0_757])).
% 2.43/3.12 cnf(i_0_1084, plain, (c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_1060,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_1071,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652,i_0_654,i_0_656,i_0_660,i_0_662,i_0_663,i_0_881,i_0_695,i_0_510,i_0_757,i_0_600])).
% 2.43/3.12 cnf(i_0_1085, 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(rename_variables,[],[i_0_620])).
% 2.43/3.12 cnf(i_0_1086, plain, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)), inference(rename_variables,[],[i_0_721])).
% 2.43/3.12 cnf(i_0_1087, 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)|X2=X1), inference(rename_variables,[],[i_0_600])).
% 2.43/3.12 cnf(i_0_1088, plain, (c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Type_Oshift(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat),v_T_H____,tc_Type_Otype),X1))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_1060,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_1071,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652,i_0_654,i_0_656,i_0_660,i_0_662,i_0_663,i_0_881,i_0_695,i_0_510,i_0_757,i_0_600,i_0_615])).
% 2.43/3.12 cnf(i_0_1089, plain, (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))))), inference(rename_variables,[],[i_0_507])).
% 2.43/3.12 cnf(i_0_1090, plain, (~hBOOL(hAPP(hAPP(c_Lambda_Obeta,X1),X2))|~c_Type_Otyping(X3,X1,X4)|c_Type_Otyping(X3,X2,X4)), inference(rename_variables,[],[i_0_615])).
% 2.43/3.12 cnf(i_0_1091, plain, (c_HOL_Ozero__class_Ozero(tc_nat)=c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|~class_Ring__and__Field_Oordered__idom(tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_1060,i_0_1086,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_620,i_0_1071,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652,i_0_654,i_0_656,i_0_660,i_0_662,i_0_663,i_0_881,i_0_695,i_0_510,i_0_757,i_0_600,i_0_615,i_0_696])).
% 2.43/3.12 cnf(i_0_1092, plain, (~c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)), inference(rename_variables,[],[i_0_721])).
% 2.43/3.12 cnf(i_0_1093, plain, (c_HOL_Oord__class_Oless(X1,X2,X3)|X1=X2|~class_Ring__and__Field_Oordered__idom(X3)|c_HOL_Oord__class_Oless(X2,X1,X3)), inference(rename_variables,[],[i_0_696])).
% 2.43/3.12 cnf(i_0_1094, plain, (hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1)=X1), inference(rename_variables,[],[i_0_766])).
% 2.43/3.12 cnf(i_0_1095, plain, (~class_Int_Onumber__ring(tc_nat)|~class_Ring__and__Field_Oidom(tc_nat)), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_758,i_0_766,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_1060,i_0_1086,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_735,i_0_620,i_0_1071,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652,i_0_654,i_0_656,i_0_660,i_0_662,i_0_663,i_0_881,i_0_695,i_0_510,i_0_757,i_0_600,i_0_615,i_0_696,i_0_657,i_0_709])).
% 2.43/3.12 cnf(i_0_1096, plain, (c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)), inference(rename_variables,[],[i_0_758])).
% 2.43/3.12 cnf(i_0_1097, plain, (X1!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))), inference(rename_variables,[],[i_0_735])).
% 2.43/3.12 cnf(i_0_1098, plain, (c_HOL_Ominus__class_Ominus(X1,X2,X3)!=c_HOL_Ozero__class_Ozero(X3)|~class_Int_Onumber__ring(X3)|X1=X2|~class_Ring__and__Field_Oidom(X3)), inference(rename_variables,[],[i_0_709])).
% 2.43/3.12 cnf(i_0_1099, plain, (~c_HOL_Oord__class_Oless(X1,X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))|c_HOL_Oord__class_Oless(X1,X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))|~c_HOL_Oord__class_Oless(X2,X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))), inference(scs_inference,[],[i_0_761,i_0_763,i_0_618,i_0_497,i_0_989,i_0_991,i_0_993,i_0_1022,i_0_1024,i_0_768,i_0_995,i_0_997,i_0_999,i_0_1001,i_0_1003,i_0_1005,i_0_1007,i_0_1009,i_0_1011,i_0_1013,i_0_1015,i_0_1017,i_0_1019,i_0_1026,i_0_1028,i_0_1039,i_0_470,i_0_758,i_0_766,i_0_559,i_0_592,i_0_551,i_0_1030,i_0_552,i_0_725,i_0_951,i_0_1050,i_0_1057,i_0_723,i_0_782,i_0_721,i_0_984,i_0_1060,i_0_1086,i_0_784,i_0_785,i_0_786,i_0_787,i_0_788,i_0_789,i_0_790,i_0_791,i_0_792,i_0_793,i_0_794,i_0_795,i_0_796,i_0_797,i_0_798,i_0_799,i_0_800,i_0_752,i_0_682,i_0_954,i_0_1049,i_0_1053,i_0_524,i_0_525,i_0_959,i_0_734,i_0_924,i_0_927,i_0_930,i_0_941,i_0_735,i_0_620,i_0_1071,i_0_729,i_0_731,i_0_636,i_0_968,i_0_637,i_0_776,i_0_675,i_0_507,i_0_456,i_0_457,i_0_458,i_0_485,i_0_486,i_0_487,i_0_607,i_0_706,i_0_722,i_0_804,i_0_806,i_0_449,i_0_501,i_0_534,i_0_554,i_0_556,i_0_583,i_0_606,i_0_621,i_0_623,i_0_630,i_0_633,i_0_635,i_0_651,i_0_599,i_0_658,i_0_708,i_0_805,i_0_843,i_0_844,i_0_845,i_0_886,i_0_846,i_0_847,i_0_848,i_0_849,i_0_850,i_0_852,i_0_853,i_0_861,i_0_862,i_0_865,i_0_866,i_0_867,i_0_868,i_0_869,i_0_870,i_0_872,i_0_873,i_0_875,i_0_876,i_0_877,i_0_882,i_0_883,i_0_884,i_0_885,i_0_529,i_0_546,i_0_547,i_0_571,i_0_572,i_0_605,i_0_614,i_0_652,i_0_654,i_0_656,i_0_660,i_0_662,i_0_663,i_0_881,i_0_695,i_0_510,i_0_757,i_0_600,i_0_615,i_0_627])).
% 2.43/3.12 cnf(i_0_1100,plain, ($false), inference(scs_inference,[],[i_0+916, i_0_919]), ['proof']).
% 2.43/3.12 % SZS output end CNFRefutation
% 2.43/3.12 % Total time : 1.273s
%------------------------------------------------------------------------------