%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL779-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:50:04 AM UTC 2026
% Result : Unsatisfiable 0.32s 0.57s
% Output : Proof 0.32s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_zero__le__imp__of__nat_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
cnf(cls_of__nat__0__le__iff_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_of__nat__0__le__iff_0) ).
cnf(cls_power__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_lessequals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_power__mono_0) ).
cnf(cls_zero__le__power_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_zero__le__power_0) ).
cnf(cls_power__inject__exp_0,axiom,
( V_m = V_n
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| c_Power_Opower__class_Opower(V_a,V_m,T_a) != c_Power_Opower__class_Opower(V_a,V_n,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_power__inject__exp_0) ).
cnf(cls_power__0_0,axiom,
( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Power_Opower(T_a) ),
file('theBenchmark.p',cls_power__0_0) ).
cnf(cls_class__semiring_Opwr__0_0,axiom,
( c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
cnf(cls_subst__lemma_0,axiom,
( c_Type_Otyping(V_e_H,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),V_T)
| ~ c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)
| ~ c_Type_Otyping(V_e_H,V_u,V_U) ),
file('theBenchmark.p',cls_subst__lemma_0) ).
cnf(cls_lift__type_0,axiom,
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,V_t),V_i),V_T) ),
file('theBenchmark.p',cls_lift__type_0) ).
cnf(cls_power__strict__decreasing_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_N,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_power__strict__decreasing_0) ).
cnf(cls_power__eq__imp__eq__base_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| V_a = V_b
| c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_Power_Opower__class_Opower(V_b,V_n,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
cnf(cls_one__less__power_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_one__less__power_0) ).
cnf(cls_lift__subst_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),V_j) ),
file('theBenchmark.p',cls_lift__subst_0) ).
cnf(cls_lift__subst__lt_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat))) ),
file('theBenchmark.p',cls_lift__subst__lt_0) ).
cnf(cls_lift_Osimps_I1_J_1,axiom,
( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat))) ),
file('theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
cnf(cls_less__add__one_0,axiom,
( c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_less__add__one_0) ).
cnf(cls_add__le__less__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__le__less__mono_0) ).
cnf(cls_add__less__le__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__less__le__mono_0) ).
cnf(cls_add__nonpos__nonpos_0,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonpos__nonpos_0) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
cnf(cls_add__nonneg__eq__0__iff_0,axiom,
( V_x = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
cnf(cls_add__nonneg__eq__0__iff_1,axiom,
( V_y = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
cnf(cls_add__increasing2_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| c_lessequals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__increasing2_0) ).
cnf(cls_add__increasing_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_b,V_c,T_a)
| c_lessequals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__increasing_0) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
cnf(cls_add__nonneg__eq__0__iff_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
cnf(cls_add__nonneg__nonneg_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonneg__nonneg_0) ).
cnf(cls_zero__less__one_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_zero__less__one_0) ).
cnf(cls_not__one__less__zero_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_not__one__less__zero_0) ).
cnf(cls_linorder__linear_0,axiom,
( c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__linear_0) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__antisym__conv2_0) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| V_x = V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__antisym__conv1_0) ).
cnf(cls_order__neq__le__trans_0,axiom,
( V_a = V_b
| ~ c_lessequals(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__neq__le__trans_0) ).
cnf(cls_order__le__neq__trans_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| V_a = V_b
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__le__neq__trans_0) ).
cnf(cls_order__less__le_2,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__less__le_2) ).
cnf(cls_order__le__less_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__le__less_0) ).
cnf(cls_xt1_I12_J_0,axiom,
( V_a = V_b
| ~ c_lessequals(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I12_J_0) ).
cnf(cls_xt1_I11_J_0,axiom,
( ~ c_lessequals(V_b,V_a,T_a)
| V_a = V_b
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I11_J_0) ).
cnf(cls_le__add__right__mono_0,axiom,
( ~ c_lessequals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| c_lessequals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__add__right__mono_0) ).
cnf(cls_order__less__le__trans_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__less__le__trans_0) ).
cnf(cls_order__le__less__trans_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__le__less__trans_0) ).
cnf(cls_order__eq__refl_0,axiom,
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__eq__refl_0) ).
cnf(cls_order__eq__iff_0,axiom,
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__eq__iff_0) ).
cnf(cls_order__trans_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__trans_0) ).
cnf(cls_xt1_I8_J_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I8_J_0) ).
cnf(cls_xt1_I7_J_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(cls_xt1_I6_J_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| c_lessequals(V_z,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I6_J_0) ).
cnf(cls_shift__gt_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat)
| hAPP(c_Type_Oshift(V_e,V_i,V_T,T_a),V_j) = hAPP(V_e,V_j) ),
file('theBenchmark.p',cls_shift__gt_0) ).
cnf(cls_add__left__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__left__mono_0) ).
cnf(cls_add__right__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__right__mono_0) ).
cnf(cls_add__le__cancel__left_0,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__le__cancel__left_0) ).
cnf(cls_add__le__cancel__left_1,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__le__cancel__left_1) ).
cnf(cls_add__le__cancel__right_0,axiom,
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__le__cancel__right_0) ).
cnf(cls_add__le__cancel__right_1,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__le__cancel__right_1) ).
cnf(cls_order__less__imp__le_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__less__imp__le_0) ).
cnf(cls_order__le__less_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__le__less_1) ).
cnf(cls_order__antisym__conv_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| V_x = V_y
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_order__antisym_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| V_x = V_y
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__antisym_0) ).
cnf(cls_order__eq__iff_2,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| V_x = V_y
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__eq__iff_2) ).
cnf(cls_gb__semiring_Osemiring__rules_I33_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_pwr,V_x),c_HOL_Oone__class_Oone(tc_nat)) = V_x ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I33_J_0) ).
cnf(cls_not__one__le__zero_0,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_not__one__le__zero_0) ).
cnf(cls_less__le__not__le_2,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_less__le__not__le_2) ).
cnf(cls_zero__le__one_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_zero__le__one_0) ).
cnf(cls_shift__eq_0,axiom,
hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T,
file('theBenchmark.p',cls_shift__eq_0) ).
cnf(cls_min__max_Ole__supE_0,axiom,
( ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a)
| c_lessequals(V_a,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__supE_0) ).
cnf(cls_min__max_Ole__supE_1,axiom,
( ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a)
| c_lessequals(V_b,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__supE_1) ).
cnf(cls_min__max_Ole__supI1_0,axiom,
( ~ c_lessequals(V_x,V_a,T_a)
| c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__supI1_0) ).
cnf(cls_min__max_Ole__supI2_0,axiom,
( ~ c_lessequals(V_x,V_b,T_a)
| c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__supI2_0) ).
cnf(cls_le__max__iff__disj_1,axiom,
( ~ c_lessequals(V_z,V_x,T_a)
| c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_le__max__iff__disj_1) ).
cnf(cls_le__max__iff__disj_2,axiom,
( ~ c_lessequals(V_z,V_y,T_a)
| c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_le__max__iff__disj_2) ).
cnf(cls_min__max_Ole__sup__iff_0,axiom,
( ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
cnf(cls_min__max_Ole__sup__iff_1,axiom,
( ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)
| c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
cnf(cls_power__one__right_0,axiom,
( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('theBenchmark.p',cls_power__one__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I33_J_0,axiom,
( c_Power_Opower__class_Opower(V_x,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_x
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
cnf(cls_le__max__iff__disj_0,axiom,
( ~ c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| c_lessequals(V_z,V_x,T_a)
| c_lessequals(V_z,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_le__max__iff__disj_0) ).
cnf(cls_le__maxI2_0,axiom,
( c_lessequals(V_y,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_le__maxI2_0) ).
cnf(cls_le__maxI1_0,axiom,
( c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_le__maxI1_0) ).
cnf(cls_min__max_Ole__supI_0,axiom,
( ~ c_lessequals(V_a,V_x,T_a)
| ~ c_lessequals(V_b,V_x,T_a)
| c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__supI_0) ).
cnf(cls_min__max_Osup__least_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_z,V_x,T_a)
| c_lessequals(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__least_0) ).
cnf(cls_min__max_Ole__sup__iff_2,axiom,
( ~ c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).
cnf(cls_one__le__power_0,axiom,
( ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| c_lessequals(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_one__le__power_0) ).
cnf(cls_add__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__mono_0) ).
cnf(cls_min__max_Ole__iff__sup_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
cnf(cls_min__max_Ole__iff__sup_1,axiom,
( c_lessequals(V_x,V_y,T_a)
| c_Orderings_Oord__class_Omax(V_x,V_y,T_a) != V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
cnf(cls_min__max_Osup__absorb1_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_x
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
cnf(cls_power__one_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('theBenchmark.p',cls_power__one_0) ).
cnf(cls_not__leE_0,axiom,
( c_lessequals(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_not__leE_0) ).
cnf(cls_linorder__antisym__conv2_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__antisym__conv2_1) ).
cnf(cls_linorder__antisym__conv1_1,axiom,
( c_lessequals(V_x,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__antisym__conv1_1) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__not__less_1) ).
cnf(cls_linorder__not__less_0,axiom,
( c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__not__less_0) ).
cnf(cls_linorder__not__le_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__not__le_1) ).
cnf(cls_linorder__not__le_0,axiom,
( c_lessequals(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__not__le_0) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_less__le__not__le_1) ).
cnf(cls_of__nat__1_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Osemiring__1(T_a) ),
file('theBenchmark.p',cls_of__nat__1_0) ).
cnf(cls_one__neq__zero_0,axiom,
( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('theBenchmark.p',cls_one__neq__zero_0) ).
cnf(cls_zero__neq__one_0,axiom,
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('theBenchmark.p',cls_zero__neq__one_0) ).
cnf(cls_add__neg__nonpos_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__neg__nonpos_0) ).
cnf(cls_add__nonpos__neg_0,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonpos__neg_0) ).
cnf(cls_add__strict__increasing_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_b,V_c,T_a)
| c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__strict__increasing_0) ).
cnf(cls_add__strict__increasing2_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
| c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__strict__increasing2_0) ).
cnf(cls_add__nonneg__pos_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonneg__pos_0) ).
cnf(cls_add__pos__nonneg_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__pos__nonneg_0) ).
cnf(cls_zero__less__two_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a)),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_zero__less__two_0) ).
cnf(cls_power__less__imp__less__base_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_power__less__imp__less__base_0) ).
cnf(cls_power__0__left_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Osemiring__0(T_a) ),
file('theBenchmark.p',cls_power__0__left_0) ).
cnf(cls_power__less__imp__less__exp_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_power__less__imp__less__exp_0) ).
cnf(cls_power__strict__increasing_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_a,V_N,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_power__strict__increasing_0) ).
cnf(cls_power__strict__increasing__iff_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_power__strict__increasing__iff_0) ).
cnf(cls_power__strict__increasing__iff_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_power__strict__increasing__iff_1) ).
cnf(cls_lift_Osimps_I3_J_0,axiom,
hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(V_s)),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,V_s),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))),
file('theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
cnf(cls_liftn_Osimps_I3_J_0,axiom,
c_Lambda_Oliftn(V_n,c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(V_n,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))),
file('theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).
cnf(cls_substn_Osimps_I3_J_0,axiom,
c_Lambda_Osubstn(c_Lambda_OdB_OAbs(V_t),V_s,V_k) = c_Lambda_OdB_OAbs(c_Lambda_Osubstn(V_t,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))),
file('theBenchmark.p',cls_substn_Osimps_I3_J_0) ).
cnf(cls_power__strict__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_power__strict__mono_0) ).
cnf(cls_subst__Abs_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(V_t)),V_s),V_k) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_s),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))),
file('theBenchmark.p',cls_subst__Abs_0) ).
cnf(cls_lift__types_0,axiom,
( ~ c_Type_Otypings(V_e,V_ts,V_Ts)
| c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts) ),
file('theBenchmark.p',cls_lift__types_0) ).
cnf(cls_substs__lemma_0,axiom,
( ~ c_Type_Otyping(V_e,V_u,V_T)
| ~ c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_T,tc_Type_Otype),V_ts,V_Ts)
| c_Type_Otypings(V_e,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts) ),
file('theBenchmark.p',cls_substs__lemma_0) ).
cnf(cls_Apps__dB__induct_5,axiom,
( ~ hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(V_P)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(V_P)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(V_P,V_t)) ),
file('theBenchmark.p',cls_Apps__dB__induct_5) ).
cnf(cls_lem_5,axiom,
( hBOOL(hAPP(V_P,V_t))
| ~ hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(V_P)),c_ListApplication_Osko__ListApplication__Xlem__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(V_P)),c_ListApplication_Osko__ListApplication__Xlem__1__4(V_P),tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('theBenchmark.p',cls_lem_5) ).
cnf(cls_nat__add__right__cancel_0,axiom,
( V_m = V_n
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k) ),
file('theBenchmark.p',cls_nat__add__right__cancel_0) ).
cnf(cls_natgb_Oadd__cancel_0,axiom,
( V_y = V_z
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_y) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z) ),
file('theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
cnf(cls_IT_Ocases_6,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_a))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)
| V_a = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))
| V_a = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_IT_Ocases_6) ).
cnf(cls_map_Osimps_I2_J_0,axiom,
c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a),
file('theBenchmark.p',cls_map_Osimps_I2_J_0) ).
cnf(cls_Cons__eq__map__conv_3,axiom,
c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a) = c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a),
file('theBenchmark.p',cls_Cons__eq__map__conv_3) ).
cnf(cls_map__eq__Cons__conv_3,axiom,
c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a),
file('theBenchmark.p',cls_map__eq__Cons__conv_3) ).
cnf(cls_rtrancl__beta__AppL_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s_H),V_t))) ),
file('theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
cnf(cls_rtrancl__beta__AppR_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t_H))) ),
file('theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
cnf(cls_append__Cons_0,axiom,
c_List_Oappend(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a),
file('theBenchmark.p',cls_append__Cons_0) ).
cnf(cls_append__eq__Cons__conv_5,axiom,
c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a),
file('theBenchmark.p',cls_append__eq__Cons__conv_5) ).
cnf(cls_add__neg__neg_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__neg__neg_0) ).
cnf(cls_listsum_Osimps_I1_J_0,axiom,
( c_List_Olistsum(c_List_Olist_ONil(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
file('theBenchmark.p',cls_listsum_Osimps_I1_J_0) ).
cnf(cls_max__less__iff__conj_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)
| c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_max__less__iff__conj_1) ).
cnf(cls_max__less__iff__conj_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_max__less__iff__conj_0) ).
cnf(cls_less__max__iff__disj_2,axiom,
( ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_less__max__iff__disj_2) ).
cnf(cls_less__max__iff__disj_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_less__max__iff__disj_1) ).
cnf(cls_min__max_Oless__supI2_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_b,T_a)
| c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oless__supI2_0) ).
cnf(cls_min__max_Oless__supI1_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_a,T_a)
| c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Oless__supI1_0) ).
cnf(cls_Snoc__step1__SnocD_1,axiom,
( ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a)
| c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)
| hBOOL(hAPP(hAPP(V_r,V_y),V_x)) ),
file('theBenchmark.p',cls_Snoc__step1__SnocD_1) ).
cnf(cls_rtranclp__converseI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y)) ),
file('theBenchmark.p',cls_rtranclp__converseI_0) ).
cnf(cls_rtranclp__converseD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x)) ),
file('theBenchmark.p',cls_rtranclp__converseD_0) ).
cnf(cls_map__is__Nil__conv_1,axiom,
c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',cls_map__is__Nil__conv_1) ).
cnf(cls_foldr_Osimps_I1_J_0,axiom,
c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a) = V_a,
file('theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),V_Q),
file('theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_add__cancel__21_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z) = V_u
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_u)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_add__cancel__21_0) ).
cnf(cls_conversepD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b))
| hBOOL(hAPP(hAPP(V_r,V_b),V_a)) ),
file('theBenchmark.p',cls_conversepD_0) ).
cnf(cls_conversep__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_r,V_b),V_a))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b)) ),
file('theBenchmark.p',cls_conversep__iff_1) ).
cnf(cls_conversep_Ocases_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a1),V_a2))
| hBOOL(hAPP(hAPP(V_r,V_a2),V_a1)) ),
file('theBenchmark.p',cls_conversep_Ocases_0) ).
cnf(cls_conversep_Ointros_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b))
| hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_b),V_a)) ),
file('theBenchmark.p',cls_conversep_Ointros_0) ).
cnf(cls_add__gr__0_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_add__gr__0_0) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_d))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_b)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_d)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c))
| ~ class_OrderedGroup_Oab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c))
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c))
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
cnf(cls_nat__add__assoc_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)),
file('theBenchmark.p',cls_nat__add__assoc_0) ).
cnf(cls_nat__add__left__commute_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)),
file('theBenchmark.p',cls_nat__add__left__commute_0) ).
cnf(cls_add__cancel__21_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z))
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_add__cancel__21_1) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_z)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(cls_xt1_I10_J_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I10_J_0) ).
cnf(cls_order__less__trans_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__less__trans_0) ).
cnf(cls_append__step1I_0,axiom,
( c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,V_x,T_a),c_List_Oappend(V_xs,V_x,T_a),T_a)
| ~ c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a) ),
file('theBenchmark.p',cls_append__step1I_0) ).
cnf(cls_append__step1I_1,axiom,
( ~ c_ListOrder_Ostep1(V_r,V_vs,V_us,T_a)
| c_ListOrder_Ostep1(V_r,c_List_Oappend(V_x,V_vs,T_a),c_List_Oappend(V_x,V_us,T_a),T_a) ),
file('theBenchmark.p',cls_append__step1I_1) ).
cnf(cls_rtrancl__beta__Abs_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_s_H))) ),
file('theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
cnf(cls_append__in__listsp__conv_0,axiom,
( ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a)
| c_List_Olistsp(V_A,V_xs,T_a) ),
file('theBenchmark.p',cls_append__in__listsp__conv_0) ).
cnf(cls_append__in__listsp__conv_1,axiom,
( ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a)
| c_List_Olistsp(V_A,V_ys,T_a) ),
file('theBenchmark.p',cls_append__in__listsp__conv_1) ).
cnf(cls_dB_Osimps_I12_J_0,axiom,
c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(V_f3,V_dB),
file('theBenchmark.p',cls_dB_Osimps_I12_J_0) ).
cnf(cls_Cons__step1__Cons_2,axiom,
( ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
| V_xs = V_ys
| V_x = V_y ),
file('theBenchmark.p',cls_Cons__step1__Cons_2) ).
cnf(cls_Cons__step1__Cons_4,axiom,
( c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_x,T_a),c_List_Olist_OCons(V_xa,V_x,T_a),T_a)
| ~ hBOOL(hAPP(hAPP(V_r,V_y),V_xa)) ),
file('theBenchmark.p',cls_Cons__step1__Cons_4) ).
cnf(cls_listsp_ONil_0,axiom,
c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a),
file('theBenchmark.p',cls_listsp_ONil_0) ).
cnf(cls_replicate__eq__replicate_0,axiom,
( V_m = V_n
| c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a) ),
file('theBenchmark.p',cls_replicate__eq__replicate_0) ).
cnf(cls_append__same__eq_0,axiom,
( V_ys = V_zs
| c_List_Oappend(V_ys,V_xs,T_a) != c_List_Oappend(V_zs,V_xs,T_a) ),
file('theBenchmark.p',cls_append__same__eq_0) ).
cnf(cls_same__append__eq_0,axiom,
( V_ys = V_zs
| c_List_Oappend(V_xs,V_ys,T_a) != c_List_Oappend(V_xs,V_zs,T_a) ),
file('theBenchmark.p',cls_same__append__eq_0) ).
cnf(cls_max__less__iff__conj_2,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_max__less__iff__conj_2) ).
cnf(cls_rtranclp_Ortrancl__refl_0,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)),
file('theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
cnf(cls_Nitpick_Ortranclp__def_1,axiom,
hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)),
file('theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
cnf(cls_accp__downwards_0,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_a,T_a)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a))
| c_Wellfounded_Oaccp(V_r,V_b,T_a) ),
file('theBenchmark.p',cls_accp__downwards_0) ).
cnf(cls_accp__downwards__aux_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a))
| ~ c_Wellfounded_Oaccp(V_r,V_a,T_a)
| c_Wellfounded_Oaccp(V_r,V_b,T_a) ),
file('theBenchmark.p',cls_accp__downwards__aux_0) ).
cnf(cls_rtranclp__trans_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_z))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_z)) ),
file('theBenchmark.p',cls_rtranclp__trans_0) ).
cnf(cls_IT__implies__termi_0,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_IT__implies__termi_0) ).
cnf(cls_termi__implies__IT_0,axiom,
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_r,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,V_r)) ),
file('theBenchmark.p',cls_termi__implies__IT_0) ).
cnf(cls_IT_Ocases_8,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_a))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)
| V_a = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a))) ),
file('theBenchmark.p',cls_IT_Ocases_8) ).
cnf(cls_append__Nil2_0,axiom,
c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a) = V_xs,
file('theBenchmark.p',cls_append__Nil2_0) ).
cnf(cls_eq__Nil__appendI_0,axiom,
V_x = c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a),
file('theBenchmark.p',cls_eq__Nil__appendI_0) ).
cnf(cls_self__append__conv_1,axiom,
V_xs = c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),
file('theBenchmark.p',cls_self__append__conv_1) ).
cnf(cls_append__Nil_0,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a) = V_ys,
file('theBenchmark.p',cls_append__Nil_0) ).
cnf(cls_self__append__conv2_1,axiom,
V_ys = c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a),
file('theBenchmark.p',cls_self__append__conv2_1) ).
cnf(cls_subst__preserves__beta2_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_r),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_i))) ),
file('theBenchmark.p',cls_subst__preserves__beta2_0) ).
cnf(cls_map__replicate_0,axiom,
c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a) = c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a),
file('theBenchmark.p',cls_map__replicate_0) ).
cnf(cls_termination__basic__simps_I1_J_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
| c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) ),
file('theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
cnf(cls_termination__basic__simps_I2_J_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat)
| c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat) ),
file('theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
cnf(cls_add__lessD1_0,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat)
| c_HOL_Oord__class_Oless(V_i,V_k,tc_nat) ),
file('theBenchmark.p',cls_add__lessD1_0) ).
cnf(cls_trans__less__add1_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m),tc_nat) ),
file('theBenchmark.p',cls_trans__less__add1_0) ).
cnf(cls_trans__less__add2_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j),tc_nat) ),
file('theBenchmark.p',cls_trans__less__add2_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
cnf(cls_nat__add__commute_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),
file('theBenchmark.p',cls_nat__add__commute_0) ).
cnf(cls_less__add__eq__less_0,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_l) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n) ),
file('theBenchmark.p',cls_less__add__eq__less_0) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_x)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_foldr__append_0,axiom,
c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a) = c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a),
file('theBenchmark.p',cls_foldr__append_0) ).
cnf(cls_Snoc__step1__SnocD_3,axiom,
( ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a)
| V_y = V_x
| hBOOL(hAPP(hAPP(V_r,V_y),V_x)) ),
file('theBenchmark.p',cls_Snoc__step1__SnocD_3) ).
cnf(cls_of__nat__eq__iff_0,axiom,
( V_m = V_n
| c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
| ~ class_Nat_Osemiring__char__0(T_a) ),
file('theBenchmark.p',cls_of__nat__eq__iff_0) ).
cnf(cls_Nil__is__map__conv_0,axiom,
( V_xs = c_List_Olist_ONil(T_b)
| c_List_Olist_ONil(T_a) != c_List_Omap(V_f,V_xs,T_b,T_a) ),
file('theBenchmark.p',cls_Nil__is__map__conv_0) ).
cnf(cls_gb__semiring_Omul__pwr_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_p)),hAPP(hAPP(V_pwr,V_x),V_q)) = hAPP(hAPP(V_pwr,V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_p),V_q)) ),
file('theBenchmark.p',cls_gb__semiring_Omul__pwr_0) ).
cnf(cls_subst__preserves__beta_H_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_t),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),V_i))) ),
file('theBenchmark.p',cls_subst__preserves__beta_H_0) ).
cnf(cls_subst__preserves__beta2_H_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_r),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_i))) ),
file('theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
cnf(cls_foldr__conv__foldl_0,axiom,
( c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,V_a,T_a,T_a) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a)
| ~ class_OrderedGroup_Oab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_foldr__conv__foldl_0) ).
cnf(cls_r__into__rtranclp_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_r,V_x),V_y))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)) ),
file('theBenchmark.p',cls_r__into__rtranclp_0) ).
cnf(cls_not__Nil__step1_0,axiom,
~ c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a),
file('theBenchmark.p',cls_not__Nil__step1_0) ).
cnf(cls_not__step1__Nil_0,axiom,
~ c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a),
file('theBenchmark.p',cls_not__step1__Nil_0) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
cnf(cls_nat__add__left__cancel_0,axiom,
( V_m = V_n
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n) ),
file('theBenchmark.p',cls_nat__add__left__cancel_0) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( V_y = V_z
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
cnf(cls_add__imp__eq_0,axiom,
( V_b = V_c
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__imp__eq_0) ).
cnf(cls_add__left__cancel_0,axiom,
( V_b = V_c
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)
| ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__left__cancel_0) ).
cnf(cls_add__right__cancel_0,axiom,
( V_b = V_c
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)
| ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__right__cancel_0) ).
cnf(cls_Cons__eq__append__conv_5,axiom,
c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a),
file('theBenchmark.p',cls_Cons__eq__append__conv_5) ).
cnf(cls_Cons__eq__appendI_0,axiom,
c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a) = c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a),
file('theBenchmark.p',cls_Cons__eq__appendI_0) ).
cnf(cls_neq__Nil__conv_1,axiom,
c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a),
file('theBenchmark.p',cls_neq__Nil__conv_1) ).
cnf(cls_list_Osimps_I3_J_0,axiom,
c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a),
file('theBenchmark.p',cls_list_Osimps_I3_J_0) ).
cnf(cls_gb__semiring_Opwr__mul_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_pwr,hAPP(hAPP(V_mul,V_x),V_y)),V_q) = hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_q)),hAPP(hAPP(V_pwr,V_y),V_q)) ),
file('theBenchmark.p',cls_gb__semiring_Opwr__mul_0) ).
cnf(cls_gb__semiring_Omul__d_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_add,V_y),V_z)) = hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_x),V_y)),hAPP(hAPP(V_mul,V_x),V_z)) ),
file('theBenchmark.p',cls_gb__semiring_Omul__d_0) ).
cnf(cls_gb__semiring_Omul__c_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,V_x),V_y) = hAPP(hAPP(V_mul,V_y),V_x) ),
file('theBenchmark.p',cls_gb__semiring_Omul__c_0) ).
cnf(cls_gb__semiring_Omul__a_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_mul,V_y),V_z)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_x),V_y)),V_z) ),
file('theBenchmark.p',cls_gb__semiring_Omul__a_0) ).
cnf(cls_gb__semiring_Omul__1_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,V_r1),V_x) = V_x ),
file('theBenchmark.p',cls_gb__semiring_Omul__1_0) ).
cnf(cls_gb__semiring_Omul__0_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,V_r0),V_x) = V_r0 ),
file('theBenchmark.p',cls_gb__semiring_Omul__0_0) ).
cnf(cls_gb__semiring_Oadd__c_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,V_x),V_y) = hAPP(hAPP(V_add,V_y),V_x) ),
file('theBenchmark.p',cls_gb__semiring_Oadd__c_0) ).
cnf(cls_gb__semiring_Oadd__a_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,V_x),hAPP(hAPP(V_add,V_y),V_z)) = hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_x),V_y)),V_z) ),
file('theBenchmark.p',cls_gb__semiring_Oadd__a_0) ).
cnf(cls_gb__semiring_Oadd__0_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,V_r0),V_x) = V_x ),
file('theBenchmark.p',cls_gb__semiring_Oadd__0_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I25_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_c),V_d)) = hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),V_d) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I24_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,V_a),V_c) = hAPP(hAPP(V_add,V_c),V_a) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I23_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),V_c) = hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),V_b) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I23_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I22_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_c),V_d)) = hAPP(hAPP(V_add,V_c),hAPP(hAPP(V_add,V_a),V_d)) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I21_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),V_c) = hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_b),V_c)) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I21_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I20_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),hAPP(hAPP(V_add,V_c),V_d)) = hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),hAPP(hAPP(V_add,V_b),V_d)) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I19_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,V_rx),hAPP(hAPP(V_mul,V_lx),V_ry)) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I19_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I18_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),V_ry) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I18_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I17_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_rx) = hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_ly),V_rx)) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I17_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I16_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_rx) = hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),V_ly) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I16_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I15_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,V_rx),hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_ry)) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I15_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I14_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_ly),hAPP(hAPP(V_mul,V_rx),V_ry))) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I14_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I13_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),hAPP(hAPP(V_mul,V_ly),V_ry)) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I13_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I12_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,V_a),V_r1) = V_a ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I12_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I11_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,V_r1),V_a) = V_a ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I11_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I10_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,V_a),V_r0) = V_r0 ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I10_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I9_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,V_r0),V_a) = V_r0 ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I9_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I8_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_b)),V_c) = hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_c)),hAPP(hAPP(V_mul,V_b),V_c)) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I8_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I7_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_mul,V_a),V_b) = hAPP(hAPP(V_mul,V_b),V_a) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I7_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I6_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,V_a),V_r0) = V_a ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I5_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,V_r0),V_a) = V_a ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I5_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I4_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,V_m),V_m) = hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_r1),V_r1)),V_m) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I4_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I3_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,V_m),hAPP(hAPP(V_mul,V_a),V_m)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_r1)),V_m) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I3_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I2_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_m)),V_m) = hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_r1)),V_m) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I2_J_0) ).
cnf(cls_gb__semiring_Osemiring__rules_I1_J_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_m)),hAPP(hAPP(V_mul,V_b),V_m)) = hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_b)),V_m) ),
file('theBenchmark.p',cls_gb__semiring_Osemiring__rules_I1_J_0) ).
cnf(cls_Cons__step1__Cons_0,axiom,
( ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
| hBOOL(hAPP(hAPP(V_r,V_y),V_x))
| V_x = V_y ),
file('theBenchmark.p',cls_Cons__step1__Cons_0) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_rtrancl__beta__App_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s_H),V_t_H))) ),
file('theBenchmark.p',cls_rtrancl__beta__App_0) ).
cnf(cls_of__nat__less__0__iff_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_of__nat__less__0__iff_0) ).
cnf(cls_min__max_Osup__commute_0,axiom,
( c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = c_Orderings_Oord__class_Omax(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__commute_0) ).
cnf(cls_liftn_Osimps_I1_J_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat)
| c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(V_i) ),
file('theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
cnf(cls_subject__reduction_H_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H))
| ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(V_e,V_t_H,V_T) ),
file('theBenchmark.p',cls_subject__reduction_H_0) ).
cnf(cls_replicate__empty_1,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',cls_replicate__empty_1) ).
cnf(cls_lift_Osimps_I1_J_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_k,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k) = c_Lambda_OdB_OVar(V_i) ),
file('theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
cnf(cls_lift__preserves__beta_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,V_r),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i))) ),
file('theBenchmark.p',cls_lift__preserves__beta_0) ).
cnf(cls_not__Cons__self2_0,axiom,
c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
file('theBenchmark.p',cls_not__Cons__self2_0) ).
cnf(cls_not__Cons__self_0,axiom,
V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
file('theBenchmark.p',cls_not__Cons__self_0) ).
cnf(cls_IT_Ocases_3,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_a))
| V_a = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))
| V_a = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_IT_Ocases_3) ).
cnf(cls_substn_Osimps_I1_J_1,axiom,
( c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_x),V_s,V_x) = c_Lambda_Oliftn(V_x,V_s,c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ),
file('theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
cnf(cls_Cons__eq__append__conv_4,axiom,
c_List_Olist_OCons(V_x,V_xs,T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a),
file('theBenchmark.p',cls_Cons__eq__append__conv_4) ).
cnf(cls_max__add__distrib__left_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Orderings_Oord__class_Omax(V_x,V_y,T_a)),V_z) = c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_max__add__distrib__left_0) ).
cnf(cls_Nil__is__map__conv_1,axiom,
c_List_Olist_ONil(T_a) = c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a),
file('theBenchmark.p',cls_Nil__is__map__conv_1) ).
cnf(cls_Snoc__step1__SnocD_0,axiom,
( ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a)
| c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)
| V_ys = V_xs ),
file('theBenchmark.p',cls_Snoc__step1__SnocD_0) ).
cnf(cls_min__max_Osup__assoc_0,axiom,
( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__assoc_0) ).
cnf(cls_min__max_Osup__left__commute_0,axiom,
( c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omax(V_y,c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
cnf(cls_Nil__is__append__conv_2,axiom,
c_List_Olist_ONil(T_a) = c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a),
file('theBenchmark.p',cls_Nil__is__append__conv_2) ).
cnf(cls_rtranclp__idemp_0,axiom,
c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a) = c_Transitive__Closure_Ortranclp(V_r,T_a),
file('theBenchmark.p',cls_rtranclp__idemp_0) ).
cnf(cls_abs_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_t))) ),
file('theBenchmark.p',cls_abs_0) ).
cnf(cls_min__max_Osup__left__idem_0,axiom,
( c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) = c_Orderings_Oord__class_Omax(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
cnf(cls_replicate__append__same_0,axiom,
c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a),
file('theBenchmark.p',cls_replicate__append__same_0) ).
cnf(cls_monoid__add_Oadd__0__right_0,axiom,
( ~ c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a)
| hAPP(hAPP(V_plus,V_a),V_zero) = V_a ),
file('theBenchmark.p',cls_monoid__add_Oadd__0__right_0) ).
cnf(cls_monoid__add_Oadd__0__left_0,axiom,
( ~ c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a)
| hAPP(hAPP(V_plus,V_zero),V_a) = V_a ),
file('theBenchmark.p',cls_monoid__add_Oadd__0__left_0) ).
cnf(cls_add__gr__0_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) ),
file('theBenchmark.p',cls_add__gr__0_2) ).
cnf(cls_add__gr__0_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat) ),
file('theBenchmark.p',cls_add__gr__0_1) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
cnf(cls_IT_Ocases_2,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_a))
| V_a = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)
| V_a = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a))) ),
file('theBenchmark.p',cls_IT_Ocases_2) ).
cnf(cls_IT_Ocases_10,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_a))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(V_a)),v_sko__InductTermi__XIT__Xcases__5(V_a)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('theBenchmark.p',cls_IT_Ocases_10) ).
cnf(cls_IT_Ocases_1,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_a))
| V_a = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)
| V_a = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(V_a)),v_sko__InductTermi__XIT__Xcases__5(V_a)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('theBenchmark.p',cls_IT_Ocases_1) ).
cnf(cls_power__eq__0__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('theBenchmark.p',cls_power__eq__0__iff_0) ).
cnf(cls_field__power__not__zero_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a) ),
file('theBenchmark.p',cls_field__power__not__zero_0) ).
cnf(cls_double__eq__0__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_double__eq__0__iff_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
cnf(cls_double__eq__0__iff_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_double__eq__0__iff_1) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x) = V_x
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
cnf(cls_comm__monoid__add_Omult__1_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
( V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a))
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
cnf(cls_add__0__left_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
file('theBenchmark.p',cls_add__0__left_0) ).
cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
file('theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
cnf(cls_neq0__conv_1,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_neq0__conv_1) ).
cnf(cls_liftn__0_0,axiom,
c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k) = V_t,
file('theBenchmark.p',cls_liftn__0_0) ).
cnf(cls_gr0I_0,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_gr0I_0) ).
cnf(cls_add__is__0_1,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_add__is__0_1) ).
cnf(cls_add__is__0_0,axiom,
( V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_add__is__0_0) ).
cnf(cls_natgb_Oadd__r0__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(tc_nat)
| V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_a) ),
file('theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
cnf(cls_add__eq__self__zero_0,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != V_m ),
file('theBenchmark.p',cls_add__eq__self__zero_0) ).
cnf(cls_add__is__0_2,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_add__is__0_2) ).
cnf(cls_gr__implies__not0_0,axiom,
~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_gr__implies__not0_0) ).
cnf(cls_not__less0_0,axiom,
~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_not__less0_0) ).
cnf(cls_even__less__0__iff_0,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_even__less__0__iff_0) ).
cnf(cls_even__less__0__iff_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_even__less__0__iff_1) ).
cnf(cls_zero__less__power_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_zero__less__power_0) ).
cnf(cls_less__max__iff__disj_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_less__max__iff__disj_0) ).
cnf(cls_substn_Osimps_I1_J_2,axiom,
( c_HOL_Oord__class_Oless(V_k,V_i,tc_nat)
| V_i = V_k
| c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_i),V_s,V_k) = c_Lambda_OdB_OVar(V_i) ),
file('theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
cnf(cls_Nil__is__append__conv_0,axiom,
( V_xs = c_List_Olist_ONil(T_a)
| c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a) ),
file('theBenchmark.p',cls_Nil__is__append__conv_0) ).
cnf(cls_Nil__is__append__conv_1,axiom,
( V_ys = c_List_Olist_ONil(T_a)
| c_List_Olist_ONil(T_a) != c_List_Oappend(V_xs,V_ys,T_a) ),
file('theBenchmark.p',cls_Nil__is__append__conv_1) ).
cnf(cls_dB_Osimps_I3_J_0,axiom,
( V_dB = V_dB_H
| c_Lambda_OdB_OAbs(V_dB) != c_Lambda_OdB_OAbs(V_dB_H) ),
file('theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
cnf(cls_append__is__Nil__conv_0,axiom,
( V_xs = c_List_Olist_ONil(T_a)
| c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a) ),
file('theBenchmark.p',cls_append__is__Nil__conv_0) ).
cnf(cls_append__is__Nil__conv_1,axiom,
( V_ys = c_List_Olist_ONil(T_a)
| c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a) ),
file('theBenchmark.p',cls_append__is__Nil__conv_1) ).
cnf(cls_conversep__eq_0,axiom,
c_Predicate_Oconversep(c_fequal(T_a),T_a,T_a) = c_fequal(T_a),
file('theBenchmark.p',cls_conversep__eq_0) ).
cnf(cls_IT_Ocases_11,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_a))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a))) ),
file('theBenchmark.p',cls_IT_Ocases_11) ).
cnf(cls_empty__replicate_1,axiom,
c_List_Olist_ONil(T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a),
file('theBenchmark.p',cls_empty__replicate_1) ).
cnf(cls_nat__less__le_1,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat),
file('theBenchmark.p',cls_nat__less__le_1) ).
cnf(cls_less__not__refl_0,axiom,
~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
file('theBenchmark.p',cls_less__not__refl_0) ).
cnf(cls_order__less__le_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__less__le_1) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__neq__iff_1) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__less__irrefl_0) ).
cnf(cls_liftn_Osimps_I1_J_1,axiom,
( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat)
| c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_n)) ),
file('theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
cnf(cls_lift__preserves__beta_H_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,V_r),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i))) ),
file('theBenchmark.p',cls_lift__preserves__beta_H_0) ).
cnf(cls_add__pos__pos_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__pos__pos_0) ).
cnf(cls_Cons__step1__Cons_3,axiom,
( ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
| V_xs = V_ys
| c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a) ),
file('theBenchmark.p',cls_Cons__step1__Cons_3) ).
cnf(cls_semigroup__add_Oadd__assoc_0,axiom,
( ~ c_OrderedGroup_Osemigroup__add(V_plus,T_a)
| hAPP(hAPP(V_plus,hAPP(hAPP(V_plus,V_a),V_b)),V_c) = hAPP(hAPP(V_plus,V_a),hAPP(hAPP(V_plus,V_b),V_c)) ),
file('theBenchmark.p',cls_semigroup__add_Oadd__assoc_0) ).
cnf(cls_listsum_Osimps_I2_J_0,axiom,
( c_List_Olistsum(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Olistsum(V_xs,T_a))
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
file('theBenchmark.p',cls_listsum_Osimps_I2_J_0) ).
cnf(cls_map__append_0,axiom,
c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a) = c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a),
file('theBenchmark.p',cls_map__append_0) ).
cnf(cls_IT_Ocases_7,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_a))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)
| V_a = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(V_a)),v_sko__InductTermi__XIT__Xcases__5(V_a)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('theBenchmark.p',cls_IT_Ocases_7) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| V_x = V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
cnf(cls_nat__neq__iff_0,axiom,
( V_m = V_n
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ),
file('theBenchmark.p',cls_nat__neq__iff_0) ).
cnf(cls_nat__less__cases_0,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| V_m = V_n
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| hBOOL(hAPP(hAPP(V_P,V_n),V_m)) ),
file('theBenchmark.p',cls_nat__less__cases_0) ).
cnf(cls_linorder__neqE__nat_0,axiom,
( V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
| c_HOL_Oord__class_Oless(V_y,V_x,tc_nat) ),
file('theBenchmark.p',cls_linorder__neqE__nat_0) ).
cnf(cls_linorder__neqE_0,axiom,
( V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__neqE_0) ).
cnf(cls_append__replicate__commute_0,axiom,
c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_k,V_x,T_a),T_a) = c_List_Oappend(c_List_Oreplicate(V_k,V_x,T_a),c_List_Oreplicate(V_n,V_x,T_a),T_a),
file('theBenchmark.p',cls_append__replicate__commute_0) ).
cnf(cls_linorder__less__linear_0,axiom,
( c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__less__linear_0) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_linorder__antisym__conv3_0) ).
cnf(cls_min__max_Osup__idem_0,axiom,
( c_Orderings_Oord__class_Omax(V_x,V_x,T_a) = V_x
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_min__max_Osup__idem_0) ).
cnf(cls_add__strict__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__strict__mono_0) ).
cnf(cls_add__less__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_l),tc_nat) ),
file('theBenchmark.p',cls_add__less__mono_0) ).
cnf(cls_list_Osimps_I2_J_0,axiom,
c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
file('theBenchmark.p',cls_list_Osimps_I2_J_0) ).
cnf(cls_of__nat__less__iff_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_of__nat__less__iff_1) ).
cnf(cls_of__nat__less__iff_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_of__nat__less__iff_0) ).
cnf(cls_listsum__foldr_0,axiom,
( c_List_Olistsum(V_xs,T_a) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a)
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
file('theBenchmark.p',cls_listsum__foldr_0) ).
cnf(cls_IT_Ocases_0,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_a))
| V_a = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)
| V_a = c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))
| V_a = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_IT_Ocases_0) ).
cnf(cls_replicate__add_0,axiom,
c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_x,T_a) = c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_m,V_x,T_a),T_a),
file('theBenchmark.p',cls_replicate__add_0) ).
cnf(cls_of__nat__0__less__iff_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_of__nat__0__less__iff_1) ).
cnf(cls_of__nat__0__less__iff_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_of__nat__0__less__iff_0) ).
cnf(cls_Snoc__step1__SnocD_2,axiom,
( ~ c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a)
| V_y = V_x
| V_ys = V_xs ),
file('theBenchmark.p',cls_Snoc__step1__SnocD_2) ).
cnf(cls_lift__map_0,axiom,
hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_t),V_i),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('theBenchmark.p',cls_lift__map_0) ).
cnf(cls_replicate__empty_0,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Oreplicate(V_n,V_x,T_a) != c_List_Olist_ONil(T_a) ),
file('theBenchmark.p',cls_replicate__empty_0) ).
cnf(cls_append__in__listsp__conv_2,axiom,
( ~ c_List_Olistsp(V_A,V_xs,T_a)
| ~ c_List_Olistsp(V_A,V_ys,T_a)
| c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a) ),
file('theBenchmark.p',cls_append__in__listsp__conv_2) ).
cnf(cls_dB_Orecs_I3_J_0,axiom,
c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a) = hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a)),
file('theBenchmark.p',cls_dB_Orecs_I3_J_0) ).
cnf(cls_semigroup__add__class_Oaxioms_0,axiom,
( c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(T_a),T_a)
| ~ class_OrderedGroup_Osemigroup__add(T_a) ),
file('theBenchmark.p',cls_semigroup__add__class_Oaxioms_0) ).
cnf(cls_empty__replicate_0,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Olist_ONil(T_a) != c_List_Oreplicate(V_n,V_x,T_a) ),
file('theBenchmark.p',cls_empty__replicate_0) ).
cnf(cls_pos__add__strict_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
| c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_pos__add__strict_0) ).
cnf(cls_foldr_Osimps_I2_J_0,axiom,
c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)),
file('theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
cnf(cls_dB_Osplit_2,axiom,
( hBOOL(hAPP(V_P,hAPP(V_f3,V_dB)))
| ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),t_a))) ),
file('theBenchmark.p',cls_dB_Osplit_2) ).
cnf(cls_dB_Osplit__asm_2,axiom,
( hBOOL(hAPP(V_P,hAPP(V_f3,V_xa)))
| ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_xa),t_a))) ),
file('theBenchmark.p',cls_dB_Osplit__asm_2) ).
cnf(cls_conversep__conversep_0,axiom,
c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a) = V_r,
file('theBenchmark.p',cls_conversep__conversep_0) ).
cnf(cls_not__add__less1_0,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat),
file('theBenchmark.p',cls_not__add__less1_0) ).
cnf(cls_not__add__less2_0,axiom,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat),
file('theBenchmark.p',cls_not__add__less2_0) ).
cnf(cls_append__self__conv_0,axiom,
( V_ys = c_List_Olist_ONil(T_a)
| c_List_Oappend(V_xs,V_ys,T_a) != V_xs ),
file('theBenchmark.p',cls_append__self__conv_0) ).
cnf(cls_self__append__conv_0,axiom,
( V_ys = c_List_Olist_ONil(T_a)
| V_xs != c_List_Oappend(V_xs,V_ys,T_a) ),
file('theBenchmark.p',cls_self__append__conv_0) ).
cnf(cls_append__self__conv2_0,axiom,
( V_xs = c_List_Olist_ONil(T_a)
| c_List_Oappend(V_xs,V_ys,T_a) != V_ys ),
file('theBenchmark.p',cls_append__self__conv2_0) ).
cnf(cls_self__append__conv2_0,axiom,
( V_xs = c_List_Olist_ONil(T_a)
| V_ys != c_List_Oappend(V_xs,V_ys,T_a) ),
file('theBenchmark.p',cls_self__append__conv2_0) ).
cnf(cls_append__eq__Cons__conv_4,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,V_xs,T_a),
file('theBenchmark.p',cls_append__eq__Cons__conv_4) ).
cnf(cls_add__strict__right__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__strict__right__mono_0) ).
cnf(cls_add__less__cancel__right_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__less__cancel__right_1) ).
cnf(cls_add__less__cancel__right_0,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__less__cancel__right_0) ).
cnf(cls_add__strict__left__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__strict__left__mono_0) ).
cnf(cls_add__less__cancel__left_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__less__cancel__left_1) ).
cnf(cls_add__less__cancel__left_0,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__less__cancel__left_0) ).
cnf(cls_add__less__mono1_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat) ),
file('theBenchmark.p',cls_add__less__mono1_0) ).
cnf(cls_nat__add__left__cancel__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
cnf(cls_nat__add__left__cancel__less_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat) ),
file('theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
cnf(cls_IT_Ocases_9,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_a))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))
| V_a = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_IT_Ocases_9) ).
cnf(cls_list_Oinject_0,axiom,
( V_a = V_a_H
| c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ),
file('theBenchmark.p',cls_list_Oinject_0) ).
cnf(cls_list_Oinject_1,axiom,
( V_list = V_list_H
| c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ),
file('theBenchmark.p',cls_list_Oinject_1) ).
cnf(cls_subject__reduction_0,axiom,
( ~ c_Type_Otyping(V_e,V_t,V_T)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H))
| c_Type_Otyping(V_e,V_t_H,V_T) ),
file('theBenchmark.p',cls_subject__reduction_0) ).
cnf(cls_Cons__step1__Cons_1,axiom,
( ~ c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)
| hBOOL(hAPP(hAPP(V_r,V_y),V_x))
| c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a) ),
file('theBenchmark.p',cls_Cons__step1__Cons_1) ).
cnf(cls_Cons__step1__Cons_5,axiom,
( ~ c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)
| c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_x,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) ),
file('theBenchmark.p',cls_Cons__step1__Cons_5) ).
cnf(cls_replicate__app__Cons__same_0,axiom,
c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a),
file('theBenchmark.p',cls_replicate__app__Cons__same_0) ).
cnf(cls_of__nat__add_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a))
| ~ class_Ring__and__Field_Osemiring__1(T_a) ),
file('theBenchmark.p',cls_of__nat__add_0) ).
cnf(cls_map__is__Nil__conv_0,axiom,
( V_xs = c_List_Olist_ONil(T_b)
| c_List_Omap(V_f,V_xs,T_b,T_a) != c_List_Olist_ONil(T_a) ),
file('theBenchmark.p',cls_map__is__Nil__conv_0) ).
cnf(cls_listsum__append_0,axiom,
( c_List_Olistsum(c_List_Oappend(V_xs,V_ys,T_a),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_List_Olistsum(V_xs,T_a)),c_List_Olistsum(V_ys,T_a))
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
file('theBenchmark.p',cls_listsum__append_0) ).
cnf(cls_append1__eq__conv_0,axiom,
( V_xs = V_ys
| c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) != c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a) ),
file('theBenchmark.p',cls_append1__eq__conv_0) ).
cnf(cls_append1__eq__conv_1,axiom,
( V_x = V_y
| c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) != c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a) ),
file('theBenchmark.p',cls_append1__eq__conv_1) ).
cnf(cls_append__is__Nil__conv_2,axiom,
c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',cls_append__is__Nil__conv_2) ).
cnf(cls_lifts__IT_0,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,V_ts,tc_Lambda_OdB)
| 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),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
file('theBenchmark.p',cls_lifts__IT_0) ).
cnf(cls_append__assoc_0,axiom,
c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a) = c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a),
file('theBenchmark.p',cls_append__assoc_0) ).
cnf(cls_append__eq__appendI_0,axiom,
c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a),
file('theBenchmark.p',cls_append__eq__appendI_0) ).
cnf(cls_append__eq__append__conv2_4,axiom,
c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a) = c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a),
file('theBenchmark.p',cls_append__eq__append__conv2_4) ).
cnf(cls_append__eq__append__conv2_5,axiom,
c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a),
file('theBenchmark.p',cls_append__eq__append__conv2_5) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_xt1_I9_J_0) ).
cnf(cls_converse__rtranclp__into__rtranclp_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_c))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c)) ),
file('theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
cnf(cls_rtranclp_Ortrancl__into__rtrancl_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(V_r,V_b),V_c))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c)) ),
file('theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
cnf(cls_accp_Ocases_0,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_a,T_a)
| ~ hBOOL(hAPP(hAPP(V_r,V_y),V_a))
| c_Wellfounded_Oaccp(V_r,V_y,T_a) ),
file('theBenchmark.p',cls_accp_Ocases_0) ).
cnf(cls_order__less__asym_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__less__asym_0) ).
cnf(cls_accp__downward_0,axiom,
( ~ c_Wellfounded_Oaccp(V_r,V_b,T_a)
| ~ hBOOL(hAPP(hAPP(V_r,V_a),V_b))
| c_Wellfounded_Oaccp(V_r,V_a,T_a) ),
file('theBenchmark.p',cls_accp__downward_0) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('theBenchmark.p',cls_order__less__asym_H_0) ).
cnf(cls_size__char_0,axiom,
c_Nat_Osize__class_Osize(V_c,tc_String_Ochar) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_size__char_0) ).
cnf(cls_replicate__eq__replicate_2,axiom,
c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a),
file('theBenchmark.p',cls_replicate__eq__replicate_2) ).
cnf(cls_max__0R_0,axiom,
c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_n,
file('theBenchmark.p',cls_max__0R_0) ).
cnf(cls_max__0L_0,axiom,
c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n,
file('theBenchmark.p',cls_max__0L_0) ).
cnf(cls_replicate__eq__replicate_1,axiom,
( V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| V_x = V_y
| c_List_Oreplicate(V_m,V_x,T_a) != c_List_Oreplicate(V_n,V_y,T_a) ),
file('theBenchmark.p',cls_replicate__eq__replicate_1) ).
cnf(cls_natgb_Oadd__r0__iff_1,axiom,
V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)),
file('theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
cnf(cls_plus__nat_Oadd__0_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n) = V_n,
file('theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
cnf(cls_Nat_Oadd__0__right_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat)) = V_m,
file('theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
cnf(cls_gb__semiring_Opwr__0_0,axiom,
( ~ c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a)
| hAPP(hAPP(V_pwr,V_x),c_HOL_Ozero__class_Ozero(tc_nat)) = V_r1 ),
file('theBenchmark.p',cls_gb__semiring_Opwr__0_0) ).
cnf(cls_foldl__foldr1_0,axiom,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_xs,T_a,T_a) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a)
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
file('theBenchmark.p',cls_foldl__foldr1_0) ).
cnf(cls_listsum_0,axiom,
( c_List_Olistsum(V_xs,T_a) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_xs,T_a,T_a)
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
file('theBenchmark.p',cls_listsum_0) ).
cnf(cls_foldl__foldr1__lemma_0,axiom,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a))
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
file('theBenchmark.p',cls_foldl__foldr1__lemma_0) ).
cnf(cls_dB_Osimps_I8_J_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != c_Lambda_OdB_OAbs(V_dB_H),
file('theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
cnf(cls_dB_Osimps_I9_J_0,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),
file('theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
cnf(cls_dB_Osplit__asm_1,axiom,
( hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xb),V_xc)))
| ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_xb),V_xc),t_a))) ),
file('theBenchmark.p',cls_dB_Osplit__asm_1) ).
cnf(cls_dB_Osplit_1,axiom,
( hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_dB1),V_dB2)))
| ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),t_a))) ),
file('theBenchmark.p',cls_dB_Osplit_1) ).
cnf(cls_lift_Osimps_I2_J_0,axiom,
hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_s),V_k)),hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),
file('theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
cnf(cls_dB_Osimps_I11_J_0,axiom,
c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(V_f2,V_dB1),V_dB2),
file('theBenchmark.p',cls_dB_Osimps_I11_J_0) ).
cnf(cls_dB_Orecs_I2_J_0,axiom,
c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a) = hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a)),
file('theBenchmark.p',cls_dB_Orecs_I2_J_0) ).
cnf(cls_appR_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_s)),hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_t))) ),
file('theBenchmark.p',cls_appR_0) ).
cnf(cls_appL_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_u)),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u))) ),
file('theBenchmark.p',cls_appL_0) ).
cnf(cls_liftn_Osimps_I2_J_0,axiom,
c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k)),
file('theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
cnf(cls_substn_Osimps_I2_J_0,axiom,
c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k)),
file('theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
cnf(cls_substn__subst__n_0,axiom,
c_Lambda_Osubstn(V_t,V_s,V_n) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat))),V_n),
file('theBenchmark.p',cls_substn__subst__n_0) ).
cnf(cls_double__induction__lemma_0,axiom,
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_s,tc_Lambda_OdB)
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_s),c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
file('theBenchmark.p',cls_double__induction__lemma_0) ).
cnf(cls_apps__preserves__beta2_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('theBenchmark.p',cls_apps__preserves__beta2_0) ).
cnf(cls_apps__preserves__betas_0,axiom,
( ~ c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,V_ss,tc_Lambda_OdB)
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('theBenchmark.p',cls_apps__preserves__betas_0) ).
cnf(cls_Abs__eq__apps__conv_1,axiom,
( V_ss = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
cnf(cls_Abs__eq__apps__conv_2,axiom,
c_Lambda_OdB_OAbs(V_r) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
cnf(cls_App__eq__foldl__conv_2,axiom,
( V_ts = c_List_Olist_ONil(tc_Lambda_OdB)
| V_r = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(V_r,V_s,V_t,V_ts),tc_Lambda_OdB,tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_App__eq__foldl__conv_2) ).
cnf(cls_ex__head__tail_0,axiom,
V_t = c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(V_t),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(V_t),tc_Lambda_OdB,tc_Lambda_OdB),
file('theBenchmark.p',cls_ex__head__tail_0) ).
cnf(cls_apps__eq__Abs__conv_1,axiom,
( V_ss = c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r) ),
file('theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
cnf(cls_apps__eq__Abs__conv_2,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OAbs(V_r),
file('theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
cnf(cls_semigroup__add_Ofoldl__assoc_0,axiom,
( ~ c_OrderedGroup_Osemigroup__add(V_plus,T_a)
| c_List_Ofoldl(V_plus,hAPP(hAPP(V_plus,V_x),V_y),V_zs,T_a,T_a) = hAPP(hAPP(V_plus,V_x),c_List_Ofoldl(V_plus,V_y,V_zs,T_a,T_a)) ),
file('theBenchmark.p',cls_semigroup__add_Ofoldl__assoc_0) ).
cnf(cls_foldl__Nil_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a,
file('theBenchmark.p',cls_foldl__Nil_0) ).
cnf(cls_foldl__assoc_0,axiom,
( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y),V_zs,T_a,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_y,V_zs,T_a,T_a))
| ~ class_OrderedGroup_Osemigroup__add(T_a) ),
file('theBenchmark.p',cls_foldl__assoc_0) ).
cnf(cls_monoid__add_Ofoldl__absorb0_0,axiom,
( ~ c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a)
| hAPP(hAPP(V_plus,V_x),c_List_Ofoldl(V_plus,V_zero,V_zs,T_a,T_a)) = c_List_Ofoldl(V_plus,V_x,V_zs,T_a,T_a) ),
file('theBenchmark.p',cls_monoid__add_Ofoldl__absorb0_0) ).
cnf(cls_foldl__Cons_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b),
file('theBenchmark.p',cls_foldl__Cons_0) ).
cnf(cls_foldl__append_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b) = c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b),
file('theBenchmark.p',cls_foldl__append_0) ).
cnf(cls_subst__map_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('theBenchmark.p',cls_subst__map_0) ).
cnf(cls_lem_3,axiom,
( hBOOL(hAPP(V_P,V_t))
| ~ hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(V_P)),c_ListApplication_Osko__ListApplication__Xlem__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(V_P,c_ListApplication_Osko__ListApplication__Xlem__1__3(V_P))) ),
file('theBenchmark.p',cls_lem_3) ).
cnf(cls_var__app__typesE_1,axiom,
( ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T)
| c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts)) ),
file('theBenchmark.p',cls_var__app__typesE_1) ).
cnf(cls_Apps__dB__induct_3,axiom,
( ~ hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(V_P)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(V_P,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(V_P)))
| hBOOL(hAPP(V_P,V_t)) ),
file('theBenchmark.p',cls_Apps__dB__induct_3) ).
cnf(cls_var__app__types_1,axiom,
( ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB),V_T)
| ~ c_Type_Otypings(V_e,V_ts,V_Ts)
| ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)
| c_Type_Otypings(V_e,V_us,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us)) ),
file('theBenchmark.p',cls_var__app__types_1) ).
cnf(cls_head__Var__reduction_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_v))
| c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v),tc_Lambda_OdB) ),
file('theBenchmark.p',cls_head__Var__reduction_0) ).
cnf(cls_IT_Ocases_4,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_a))
| V_a = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(V_a)),v_sko__InductTermi__XIT__Xcases__5(V_a)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('theBenchmark.p',cls_IT_Ocases_4) ).
cnf(cls_subst__preserves__beta_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_t),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),V_i))) ),
file('theBenchmark.p',cls_subst__preserves__beta_0) ).
cnf(cls_subst__lift_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k) = V_t,
file('theBenchmark.p',cls_subst__lift_0) ).
cnf(cls_IT_Ocases_5,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_a))
| V_a = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a))) ),
file('theBenchmark.p',cls_IT_Ocases_5) ).
cnf(cls_dB_Osimps_I7_J_0,axiom,
c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat),
file('theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
cnf(cls_dB_Osplit__asm_0,axiom,
( hBOOL(hAPP(V_P,hAPP(V_f1,V_xd)))
| ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_xd),t_a))) ),
file('theBenchmark.p',cls_dB_Osplit__asm_0) ).
cnf(cls_dB_Osplit_0,axiom,
( hBOOL(hAPP(V_P,hAPP(V_f1,V_nat)))
| ~ hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),t_a))) ),
file('theBenchmark.p',cls_dB_Osplit_0) ).
cnf(cls_beta__cases_I1_J_0,axiom,
~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)),
file('theBenchmark.p',cls_beta__cases_I1_J_0) ).
cnf(cls_dB_Orecs_I1_J_0,axiom,
c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat),
file('theBenchmark.p',cls_dB_Orecs_I1_J_0) ).
cnf(cls_dB_Osimps_I6_J_0,axiom,
c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H),
file('theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
cnf(cls_typing__elims_I1_J_0,axiom,
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| hAPP(V_e,V_i) = V_T ),
file('theBenchmark.p',cls_typing__elims_I1_J_0) ).
cnf(cls_dB_Osimps_I10_J_0,axiom,
c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a) = hAPP(V_f1,V_nat),
file('theBenchmark.p',cls_dB_Osimps_I10_J_0) ).
cnf(cls_typing_OVar_0,axiom,
c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)),
file('theBenchmark.p',cls_typing_OVar_0) ).
cnf(cls_lift__IT_0,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i))) ),
file('theBenchmark.p',cls_lift__IT_0) ).
cnf(cls_Lambda_0,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_r))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r))) ),
file('theBenchmark.p',cls_Lambda_0) ).
cnf(cls_beta_0,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat)))),
file('theBenchmark.p',cls_beta_0) ).
cnf(cls_head__Var__reduction_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),V_v))
| V_v = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v),tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_head__Var__reduction_1) ).
cnf(cls_power__eq__0__iff_2,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('theBenchmark.p',cls_power__eq__0__iff_2) ).
cnf(cls_power__0__left_1,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Osemiring__0(T_a) ),
file('theBenchmark.p',cls_power__0__left_1) ).
cnf(cls_power__eq__0__iff_1,axiom,
( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('theBenchmark.p',cls_power__eq__0__iff_1) ).
cnf(cls_of__nat__0_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Osemiring__1(T_a) ),
file('theBenchmark.p',cls_of__nat__0_0) ).
cnf(cls_foldl__absorb0_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_zs,T_a,T_a)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_x,V_zs,T_a,T_a)
| ~ class_OrderedGroup_Omonoid__add(T_a) ),
file('theBenchmark.p',cls_foldl__absorb0_0) ).
cnf(cls_substn__subst__0_0,axiom,
c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)),
file('theBenchmark.p',cls_substn__subst__0_0) ).
cnf(cls_dB_Osize_I4_J_0,axiom,
c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(V_nat),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_dB_Osize_I4_J_0) ).
cnf(cls_dB_Osize_I1_J_0,axiom,
c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(V_nat)) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_dB_Osize_I1_J_0) ).
cnf(cls_App__eq__foldl__conv_4,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('theBenchmark.p',cls_App__eq__foldl__conv_4) ).
cnf(cls_App__eq__foldl__conv_0,axiom,
( hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) = V_t
| hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_App__eq__foldl__conv_0) ).
cnf(cls_apps__eq__Abs__conv_0,axiom,
( V_s = c_Lambda_OdB_OAbs(V_r)
| c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(V_r) ),
file('theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
cnf(cls_Abs__apps__eq__Abs__apps__conv_0,axiom,
( V_r = V_s
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
cnf(cls_Abs__apps__eq__Abs__apps__conv_1,axiom,
( V_rs = V_ss
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
cnf(cls_apps__preserves__beta_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('theBenchmark.p',cls_apps__preserves__beta_0) ).
cnf(cls_Abs__eq__apps__conv_0,axiom,
( c_Lambda_OdB_OAbs(V_r) = V_s
| c_Lambda_OdB_OAbs(V_r) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
cnf(cls_subst__lt_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_j,V_i,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_j)),V_u),V_i) = c_Lambda_OdB_OVar(V_j) ),
file('theBenchmark.p',cls_subst__lt_0) ).
cnf(cls_subst__Var_2,axiom,
( c_HOL_Oord__class_Oless(V_k,V_i,tc_nat)
| V_i = V_k
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i)),V_s),V_k) = c_Lambda_OdB_OVar(V_i) ),
file('theBenchmark.p',cls_subst__Var_2) ).
cnf(cls_subst__Var_1,axiom,
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_x)),V_s),V_x) = V_s
| c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ),
file('theBenchmark.p',cls_subst__Var_1) ).
cnf(cls_var__app__type__eq_0,axiom,
( ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T)
| ~ c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)
| V_T = V_U ),
file('theBenchmark.p',cls_var__app__type__eq_0) ).
cnf(cls_Var__apps__neq__Abs__apps_0,axiom,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
file('theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
cnf(cls_Var__eq__apps__conv_2,axiom,
c_Lambda_OdB_OVar(V_m) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('theBenchmark.p',cls_Var__eq__apps__conv_2) ).
cnf(cls_Var__eq__apps__conv_1,axiom,
( V_ss = c_List_Olist_ONil(tc_Lambda_OdB)
| c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_Var__eq__apps__conv_1) ).
cnf(cls_Abs__App__neq__Var__apps_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),
file('theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
cnf(cls_IT_OVar_0,axiom,
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('theBenchmark.p',cls_IT_OVar_0) ).
cnf(cls_Beta_0,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_s),c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_s))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('theBenchmark.p',cls_Beta_0) ).
cnf(cls_subst__App_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_s),V_k) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_k)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_s),V_k)),
file('theBenchmark.p',cls_subst__App_0) ).
cnf(cls_dB_Osimps_I1_J_0,axiom,
( V_nat = V_nat_H
| c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OVar(V_nat_H) ),
file('theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
cnf(cls_Var__apps__eq__Var__apps__conv_0,axiom,
( V_m = V_n
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
cnf(cls_Var__apps__eq__Var__apps__conv_1,axiom,
( V_rs = V_ss
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
cnf(cls_subst__eq_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u,
file('theBenchmark.p',cls_subst__eq_0) ).
cnf(cls_subst__Var__IT_0,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_r))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),c_Lambda_OdB_OVar(V_i)),V_j))) ),
file('theBenchmark.p',cls_subst__Var__IT_0) ).
cnf(cls_dB_Osimps_I2_J_0,axiom,
( V_dB1 = V_dB1_H
| hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ),
file('theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
cnf(cls_dB_Osimps_I2_J_1,axiom,
( V_dB2 = V_dB2_H
| hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) ),
file('theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
cnf(cls_Var__eq__apps__conv_0,axiom,
( c_Lambda_OdB_OVar(V_m) = V_s
| c_Lambda_OdB_OVar(V_m) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_Var__eq__apps__conv_0) ).
cnf(cls_dB_Osimps_I4_J_0,axiom,
c_Lambda_OdB_OVar(V_nat) != hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H),
file('theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
cnf(cls_Var__IT_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))),
file('theBenchmark.p',cls_Var__IT_0) ).
cnf(cls_apps__eq__tail__conv_0,axiom,
( V_r = V_s
| c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ts,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ts,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_apps__eq__tail__conv_0) ).
cnf(cls_dB_Osimps_I5_J_0,axiom,
hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H) != c_Lambda_OdB_OVar(V_nat),
file('theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
cnf(cls_conjecture_0,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_2,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_3,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,v_s),c_Lambda_OdB_OVar(v_i)))),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_4,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,v_s)),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(clsarity_fun__Orderings_Opreorder,axiom,
( ~ class_Orderings_Opreorder(T_1)
| class_Orderings_Opreorder(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( ~ class_Orderings_Oorder(T_1)
| class_Orderings_Oorder(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
file('theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
file('theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
cnf(clsarity_nat__Power_Opower,axiom,
class_Power_Opower(tc_nat),
file('theBenchmark.p',clsarity_nat__Power_Opower) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)),
file('theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_fequal(T_a),V_X),V_Y))
| V_X = V_Y ),
file('theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
cnf(cls_add__nonneg__eq__0__iff_2_simplified,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
inference(simplify_clause,[status(thm)],[cls_add__nonneg__eq__0__iff_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( c_HOL_Ozero__class_Ozero(Eq_x_0) = c_HOL_Ozero__class_Ozero(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(Eq_x_0,Eq_x_1) = c_Nat_Osemiring__1__class_Oof__nat(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( c_Power_Opower__class_Opower(Eq_x_0,Eq_x_1,Eq_x_2) = c_Power_Opower__class_Opower(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( c_HOL_Oone__class_Oone(Eq_x_0) = c_HOL_Oone__class_Oone(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( c_Type_Oshift(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Type_Oshift(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( hAPP(Eq_x_0,Eq_x_1) = hAPP(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( c_HOL_Oplus__class_Oplus(Eq_x_0) = c_HOL_Oplus__class_Oplus(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( c_Lambda_OdB_OVar(Eq_x_0) = c_Lambda_OdB_OVar(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( c_Orderings_Oord__class_Omax(Eq_x_0,Eq_x_1,Eq_x_2) = c_Orderings_Oord__class_Omax(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( c_Lambda_OdB_OAbs(Eq_x_0) = c_Lambda_OdB_OAbs(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( c_Lambda_Oliftn(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lambda_Oliftn(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( c_Lambda_Osubstn(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lambda_Osubstn(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( c_COMBC(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_COMBC(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( c_List_Omap(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_List_Omap(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( tc_fun(Eq_x_0,Eq_x_1) = tc_fun(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(Eq_x_0) = c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(Eq_x_0) = c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( c_List_Ofoldl(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_List_Ofoldl(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(Eq_x_0) = c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(Eq_x_0) = c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( c_ListApplication_Osko__ListApplication__Xlem__1__3(Eq_x_0) = c_ListApplication_Osko__ListApplication__Xlem__1__3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( c_ListApplication_Osko__ListApplication__Xlem__1__4(Eq_x_0) = c_ListApplication_Osko__ListApplication__Xlem__1__4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( c_ListApplication_Osko__ListApplication__Xlem__1__1(Eq_x_0) = c_ListApplication_Osko__ListApplication__Xlem__1__1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( c_ListApplication_Osko__ListApplication__Xlem__1__2(Eq_x_0) = c_ListApplication_Osko__ListApplication__Xlem__1__2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( v_sko__InductTermi__XIT__Xcases__4(Eq_x_0) = v_sko__InductTermi__XIT__Xcases__4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( v_sko__InductTermi__XIT__Xcases__5(Eq_x_0) = v_sko__InductTermi__XIT__Xcases__5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( v_sko__InductTermi__XIT__Xcases__6(Eq_x_0) = v_sko__InductTermi__XIT__Xcases__6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( v_sko__InductTermi__XIT__Xcases__3(Eq_x_0) = v_sko__InductTermi__XIT__Xcases__3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( v_sko__InductTermi__XIT__Xcases__1(Eq_x_0) = v_sko__InductTermi__XIT__Xcases__1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( c_List_Olist_OCons(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Olist_OCons(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( c_Transitive__Closure_Ortranclp(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Ortranclp(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( c_List_Oappend(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Oappend(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( c_List_Olist_ONil(Eq_x_0) = c_List_Olist_ONil(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( c_List_Olistsum(Eq_x_0,Eq_x_1) = c_List_Olistsum(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( c_Predicate_Oconversep(Eq_x_0,Eq_x_1,Eq_x_2) = c_Predicate_Oconversep(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( c_List_Ofoldr(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_List_Ofoldr(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( c_Lambda_OdB_OdB__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Lambda_OdB_OdB__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( c_List_Oreplicate(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Oreplicate(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( v_sko__InductTermi__XIT__Xcases__2(Eq_x_0) = v_sko__InductTermi__XIT__Xcases__2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( c_fequal(Eq_x_0) = c_fequal(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( c_Lambda_OdB_OdB__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Lambda_OdB_OdB__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( c_Nat_Osize__class_Osize(Eq_x_0,Eq_x_1) = c_Nat_Osize__class_Osize(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(Eq_x_0) = c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(Eq_x_0) = c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( c_Type_Osko__Type__Xvar__app__typesE__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Type_Osko__Type__Xvar__app__typesE__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,axiom,
( c_Type_Osko__Type__Xvar__app__types__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Type_Osko__Type__Xvar__app__types__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_51,axiom,
( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( c_Lambda_OdB_OdB__size(Eq_x_0) = c_Lambda_OdB_OdB__size(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( class_Ring__and__Field_Oordered__semidom(Eq_y_0)
| ~ class_Ring__and__Field_Oordered__semidom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( c_lessequals(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_lessequals(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_55,axiom,
( c_HOL_Oord__class_Oless(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_HOL_Oord__class_Oless(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_56,axiom,
( class_Power_Opower(Eq_y_0)
| ~ class_Power_Opower(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_57,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(Eq_y_0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_58,axiom,
( c_Type_Otyping(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Type_Otyping(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_59,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(Eq_y_0)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_60,axiom,
( class_OrderedGroup_Opordered__comm__monoid__add(Eq_y_0)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_61,axiom,
( class_OrderedGroup_Olordered__ab__group__add(Eq_y_0)
| ~ class_OrderedGroup_Olordered__ab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_62,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(Eq_y_0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_63,axiom,
( class_OrderedGroup_Ocomm__monoid__add(Eq_y_0)
| ~ class_OrderedGroup_Ocomm__monoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_64,axiom,
( class_Orderings_Olinorder(Eq_y_0)
| ~ class_Orderings_Olinorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_65,axiom,
( class_Orderings_Oorder(Eq_y_0)
| ~ class_Orderings_Oorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_66,axiom,
( class_OrderedGroup_Opordered__ab__group__add(Eq_y_0)
| ~ class_OrderedGroup_Opordered__ab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_67,axiom,
( class_Orderings_Opreorder(Eq_y_0)
| ~ class_Orderings_Opreorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_68,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(Eq_y_0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_69,axiom,
( c_Groebner__Basis_Ogb__semiring(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ c_Groebner__Basis_Ogb__semiring(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_70,axiom,
( class_OrderedGroup_Omonoid__mult(Eq_y_0)
| ~ class_OrderedGroup_Omonoid__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_71,axiom,
( class_Ring__and__Field_Osemiring__1(Eq_y_0)
| ~ class_Ring__and__Field_Osemiring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_72,axiom,
( class_Ring__and__Field_Ozero__neq__one(Eq_y_0)
| ~ class_Ring__and__Field_Ozero__neq__one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_73,axiom,
( class_Ring__and__Field_Osemiring__0(Eq_y_0)
| ~ class_Ring__and__Field_Osemiring__0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_74,axiom,
( c_Type_Otypings(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Type_Otypings(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_75,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_76,axiom,
( c_List_Olistsp(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_List_Olistsp(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_77,axiom,
( class_OrderedGroup_Omonoid__add(Eq_y_0)
| ~ class_OrderedGroup_Omonoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_78,axiom,
( c_ListOrder_Ostep1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ c_ListOrder_Ostep1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_79,axiom,
( class_OrderedGroup_Oab__group__add(Eq_y_0)
| ~ class_OrderedGroup_Oab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_80,axiom,
( class_OrderedGroup_Oab__semigroup__add(Eq_y_0)
| ~ class_OrderedGroup_Oab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_81,axiom,
( c_Wellfounded_Oaccp(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Wellfounded_Oaccp(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_82,axiom,
( class_Nat_Osemiring__char__0(Eq_y_0)
| ~ class_Nat_Osemiring__char__0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_83,axiom,
( class_Ring__and__Field_Oidom(Eq_y_0)
| ~ class_Ring__and__Field_Oidom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_84,axiom,
( class_Int_Onumber__ring(Eq_y_0)
| ~ class_Int_Onumber__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_85,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(Eq_y_0)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_86,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(Eq_y_0)
| ~ class_OrderedGroup_Ocancel__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_87,axiom,
( c_OrderedGroup_Omonoid__add(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_OrderedGroup_Omonoid__add(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_88,axiom,
( class_Ring__and__Field_Ono__zero__divisors(Eq_y_0)
| ~ class_Ring__and__Field_Ono__zero__divisors(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_89,axiom,
( class_Ring__and__Field_Omult__zero(Eq_y_0)
| ~ class_Ring__and__Field_Omult__zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_90,axiom,
( class_Ring__and__Field_Oring__1__no__zero__divisors(Eq_y_0)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_91,axiom,
( class_Ring__and__Field_Oordered__idom(Eq_y_0)
| ~ class_Ring__and__Field_Oordered__idom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_92,axiom,
( c_OrderedGroup_Osemigroup__add(Eq_y_0,Eq_y_1)
| ~ c_OrderedGroup_Osemigroup__add(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_93,axiom,
( class_OrderedGroup_Osemigroup__add(Eq_y_0)
| ~ class_OrderedGroup_Osemigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL779-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 15:54:48 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.32/0.57 % SZS status Unsatisfiable for theBenchmark
% 0.32/0.57 % SZS output start Proof for theBenchmark
% See solution above
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