%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWV884-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 09:04:28 AM UTC 2026
% Result : Unsatisfiable 150.16s 150.45s
% Output : Proof 150.29s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_dvd__mult__cancel2_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_m,tc_nat),V_m,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ),
file('theBenchmark.p',cls_dvd__mult__cancel2_1) ).
cnf(cls_dvd__mult__cancel1_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_m,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ),
file('theBenchmark.p',cls_dvd__mult__cancel1_1) ).
cnf(cls_less__Suc0_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_less__Suc0_0) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_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),c_HOL_Oplus__class_Oplus(V_a,V_a,T_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_mult__le__cancel2_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__le__cancel2_1) ).
cnf(cls_mult__le__cancel1_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__le__cancel1_1) ).
cnf(cls_Diff__triv_0,axiom,
( c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = V_A
| c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Diff__triv_0) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(cls_nat__mult__commute_0,axiom,
c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),
file('theBenchmark.p',cls_nat__mult__commute_0) ).
cnf(cls_double__eq__0__iff_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),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_add__is__0_2,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_add__is__0_2) ).
cnf(cls_add__nonneg__eq__0__iff_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),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_class__semiring_Osemiring__rules_I7_J_0,axiom,
( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
cnf(cls_mod__add__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__eq_0) ).
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),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__nonneg__nonneg_0) ).
cnf(cls_finite__vimageI_0,axiom,
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a)
| c_Finite__Set_Ofinite(c_Set_Ovimage(V_h,V_F,T_b,T_a),T_b) ),
file('theBenchmark.p',cls_finite__vimageI_0) ).
cnf(cls_mult__eq__if_1,axiom,
( V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__eq__if_1) ).
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_psubset__trans_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(V_B,V_C,tc_fun(T_a,tc_bool))
| c_HOL_Oord__class_Oless(V_A,V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_psubset__trans_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_class__semiring_Oadd__a_0,axiom,
( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(cls_add__cancel__21_1,axiom,
( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_add__cancel__21_1) ).
cnf(cls_nat__add__left__commute_0,axiom,
c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat),tc_nat),
file('theBenchmark.p',cls_nat__add__left__commute_0) ).
cnf(cls_nat__add__assoc_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat),
file('theBenchmark.p',cls_nat__add__assoc_0) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Oab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a)
| ~ 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_I22_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a)
| ~ 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_I21_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
cnf(cls_add__gr__0_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),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_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_dvd__1__left_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat),
file('theBenchmark.p',cls_dvd__1__left_0) ).
cnf(cls_add__cancel__21_0,axiom,
( c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_y,V_u,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_add__cancel__21_0) ).
cnf(cls_Diff__idemp_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__idemp_0) ).
cnf(cls_mod__less__divisor_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_mod__less__divisor_0) ).
cnf(cls_add__inf__distrib__left_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_b,V_c,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a) ),
file('theBenchmark.p',cls_add__inf__distrib__left_0) ).
cnf(cls_add__inf__distrib__right_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a) ),
file('theBenchmark.p',cls_add__inf__distrib__right_0) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_b,V_c,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).
cnf(cls_dvd_Oless__trans_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat) ),
file('theBenchmark.p',cls_dvd_Oless__trans_1) ).
cnf(cls_mod__add__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__left__eq_0) ).
cnf(cls_mod__add__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__right__eq_0) ).
cnf(cls_nat__mult__eq__1__iff_1,axiom,
( V_n = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
file('theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).
cnf(cls_nat__mult__eq__1__iff_0,axiom,
( V_m = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
file('theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).
cnf(cls_one__is__add_5,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('theBenchmark.p',cls_one__is__add_5) ).
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,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),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_diff__add__0_0,axiom,
c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_diff__add__0_0) ).
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_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_nat__mult__eq__cancel1_0,axiom,
( V_m = V_n
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
cnf(cls_one__is__add_3,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_one__is__add_3) ).
cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
cnf(cls_natgb_Onoteq__reduce_1,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),tc_nat),
file('theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).
cnf(cls_natgb_Oadd__mul__solve_1,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat),
file('theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).
cnf(cls_mod__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__0_0) ).
cnf(cls_Suc__eq__plus1_0,axiom,
c_Suc(V_n) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('theBenchmark.p',cls_Suc__eq__plus1_0) ).
cnf(cls_Suc__eq__plus1__left_0,axiom,
c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat),
file('theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
cnf(cls_mod__mod__trivial_0,axiom,
( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mod__trivial_0) ).
cnf(cls_add__is__1_4,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('theBenchmark.p',cls_add__is__1_4) ).
cnf(cls_dvd__triv__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__triv__right_0) ).
cnf(cls_dvd__triv__left_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__triv__left_0) ).
cnf(cls_dvdI_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a)
| ~ class_Ring__and__Field_Odvd(T_a) ),
file('theBenchmark.p',cls_dvdI_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,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),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_class__semiring_Osemiring__rules_I11_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
cnf(cls_mult__1__right_0,axiom,
( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('theBenchmark.p',cls_mult__1__right_0) ).
cnf(cls_mult__1__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('theBenchmark.p',cls_mult__1__left_0) ).
cnf(cls_mult__1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a
| ~ class_OrderedGroup_Ocomm__monoid__mult(T_a) ),
file('theBenchmark.p',cls_mult__1_0) ).
cnf(cls_nat__mult__1_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) = V_n,
file('theBenchmark.p',cls_nat__mult__1_0) ).
cnf(cls_nat__mult__1__right_0,axiom,
c_HOL_Otimes__class_Otimes(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = V_n,
file('theBenchmark.p',cls_nat__mult__1__right_0) ).
cnf(cls_class__semiring_Omul__1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a) = V_x
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Omul__1_0) ).
cnf(cls_psubset__insert__iff_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a)
| ~ c_in(V_x,V_A,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_psubset__insert__iff_1) ).
cnf(cls_psubset__insert__iff_4,axiom,
( c_in(V_x,V_B,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_psubset__insert__iff_4) ).
cnf(cls_eq__add__iff1_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('theBenchmark.p',cls_eq__add__iff1_1) ).
cnf(cls_inj__on__diff_0,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| c_Fun_Oinj__on(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b) ),
file('theBenchmark.p',cls_inj__on__diff_0) ).
cnf(cls_dvd__mult__cancel__right_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
cnf(cls_dvd__mult__cancel__left_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
cnf(cls_nat__mult__dvd__cancel__disj_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__mult__dvd__cancel__disj_2) ).
cnf(cls_zmod__simps_I4_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_zmod__simps_I4_J_0) ).
cnf(cls_mult__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(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__strict__mono_0) ).
cnf(cls_vimage__Diff_0,axiom,
c_Set_Ovimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_vimage__Diff_0) ).
cnf(cls_psubset__insert__iff_8,axiom,
( ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_psubset__insert__iff_8) ).
cnf(cls_eq__add__iff2_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('theBenchmark.p',cls_eq__add__iff2_1) ).
cnf(cls_nat__less__add__iff1_0,axiom,
( ~ c_lessequals(V_j,V_i,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__less__add__iff1_0) ).
cnf(cls_nat__less__add__iff1_1,axiom,
( ~ c_lessequals(V_j,V_i,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__less__add__iff1_1) ).
cnf(cls_nat__less__add__iff2_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__less__add__iff2_0) ).
cnf(cls_nat__less__add__iff2_1,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__less__add__iff2_1) ).
cnf(cls_eq__add__iff2_0,axiom,
( V_c = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('theBenchmark.p',cls_eq__add__iff2_0) ).
cnf(cls_eq__add__iff1_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) = V_d
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Oring(T_a) ),
file('theBenchmark.p',cls_eq__add__iff1_0) ).
cnf(cls_less__add__Suc1_0,axiom,
c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat),
file('theBenchmark.p',cls_less__add__Suc1_0) ).
cnf(cls_less__add__Suc2_0,axiom,
c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat),
file('theBenchmark.p',cls_less__add__Suc2_0) ).
cnf(cls_less__iff__Suc__add_1,axiom,
c_HOL_Oord__class_Oless(V_m,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)),tc_nat),
file('theBenchmark.p',cls_less__iff__Suc__add_1) ).
cnf(cls_inj__vimage__image__eq_0,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| c_Set_Ovimage(V_f,c_Set_Oimage(V_f,V_A,T_a,T_b),T_a,T_b) = V_A ),
file('theBenchmark.p',cls_inj__vimage__image__eq_0) ).
cnf(cls_vimage__UNIV_0,axiom,
c_Set_Ovimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_vimage__UNIV_0) ).
cnf(cls_Diff__insert_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__insert_0) ).
cnf(cls_Diff__insert2_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__insert2_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,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),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_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,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),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_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,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),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,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
cnf(cls_add__lessD1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),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,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),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,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_trans__less__add2_0) ).
cnf(cls_dvd__mod__imp__dvd_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).
cnf(cls_dvd__mod__iff_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__mod__iff_1) ).
cnf(cls_dvd__mod__iff_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__mod__iff_0) ).
cnf(cls_dvd__mod_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__mod_0) ).
cnf(cls_Suc__times__mod__eq_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),V_k,tc_nat)
| c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)),V_k,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
file('theBenchmark.p',cls_Suc__times__mod__eq_0) ).
cnf(cls_nat__1__eq__mult__iff_2,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('theBenchmark.p',cls_nat__1__eq__mult__iff_2) ).
cnf(cls_inv__into__f__f_0,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_in(V_x,V_A,T_a)
| hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),hAPP(V_f,V_x)) = V_x ),
file('theBenchmark.p',cls_inv__into__f__f_0) ).
cnf(cls_inv__into__f__eq_0,axiom,
( hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_aa,T_a),hAPP(V_f,V_x)) = V_x
| ~ c_Fun_Oinj__on(V_f,V_A,T_aa,T_a)
| ~ c_in(V_x,V_A,T_aa) ),
file('theBenchmark.p',cls_inv__into__f__eq_0) ).
cnf(cls_sum__squares__ge__zero_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__ge__zero_0) ).
cnf(cls_mod__by__0_0,axiom,
( c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__by__0_0) ).
cnf(cls_mod__self_0,axiom,
( c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__self_0) ).
cnf(cls_inf__bot__right_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Orderings_Obot__class_Obot(T_a),T_a) = c_Orderings_Obot__class_Obot(T_a)
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_inf__bot__right_0) ).
cnf(cls_inf__bot__left_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) = c_Orderings_Obot__class_Obot(T_a)
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_inf__bot__left_0) ).
cnf(cls_Int__empty__left_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__empty__left_0) ).
cnf(cls_Int__empty__right_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__empty__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_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,
( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_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,
c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),
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)
| c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_less__add__eq__less_0) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_mult__eq__1__iff_0,axiom,
( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_mult__eq__1__iff_0) ).
cnf(cls_mult__eq__1__iff_1,axiom,
( V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_mult__eq__1__iff_1) ).
cnf(cls_mod__le__divisor_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_mod__le__divisor_0) ).
cnf(cls_card__Suc__eq_3,axiom,
( c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(V_A,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| c_Finite__Set_Ocard(V_A,T_a) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_card__Suc__eq_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_class__ringb_Oadd__r0__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_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_add__eq__self__zero_0,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != V_m ),
file('theBenchmark.p',cls_add__eq__self__zero_0) ).
cnf(cls_natgb_Oadd__r0__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(tc_nat)
| V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat) ),
file('theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
cnf(cls_image__Int_0,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| c_Set_Oimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(V_f,V_A,T_a,T_b),c_Set_Oimage(V_f,V_B,T_a,T_b),tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_image__Int_0) ).
cnf(cls_mult__less__imp__less__right_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__imp__less__right_0) ).
cnf(cls_mult__less__imp__less__left_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__imp__less__left_0) ).
cnf(cls_mult__right__less__imp__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semiring(T_a) ),
file('theBenchmark.p',cls_mult__right__less__imp__less_0) ).
cnf(cls_mult__left__less__imp__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semiring(T_a) ),
file('theBenchmark.p',cls_mult__left__less__imp__less_0) ).
cnf(cls_mod__mult__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__eq_0) ).
cnf(cls_nat__mult__eq__cancel__disj_0,axiom,
( V_k = c_HOL_Ozero__class_Ozero(tc_nat)
| V_m = V_n
| c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
cnf(cls_mult__cancel1_0,axiom,
( V_m = V_n
| V_k = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat) != c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_mult__cancel1_0) ).
cnf(cls_mult__cancel2_0,axiom,
( V_m = V_n
| V_k = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat) != c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat) ),
file('theBenchmark.p',cls_mult__cancel2_0) ).
cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_m,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
cnf(cls_Diff__empty_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A,
file('theBenchmark.p',cls_Diff__empty_0) ).
cnf(cls_Diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__cancel_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)
| c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != 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__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)
| c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != 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__is__0_0,axiom,
( V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_add__is__0_0) ).
cnf(cls_add__is__0_1,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_add__is__0_1) ).
cnf(cls_double__eq__0__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_a,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_0) ).
cnf(cls_One__nat__def_0,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('theBenchmark.p',cls_One__nat__def_0) ).
cnf(cls_less__add__iff2_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_less__add__iff2_1) ).
cnf(cls_one__is__add_0,axiom,
( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_one__is__add_0) ).
cnf(cls_Max__singleton_0,axiom,
( c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_Max__singleton_0) ).
cnf(cls_mult__less__cancel2_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ),
file('theBenchmark.p',cls_mult__less__cancel2_0) ).
cnf(cls_mult__less__cancel1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ),
file('theBenchmark.p',cls_mult__less__cancel1_0) ).
cnf(cls_of__nat__Suc_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(V_m),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a)
| ~ class_Ring__and__Field_Osemiring__1(T_a) ),
file('theBenchmark.p',cls_of__nat__Suc_0) ).
cnf(cls_mult__le__cancel2_0,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_mult__le__cancel2_0) ).
cnf(cls_mult__le__cancel1_0,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_mult__le__cancel1_0) ).
cnf(cls_nat__mult__le__cancel1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__mult__le__cancel1_0) ).
cnf(cls_nat__mult__le__cancel1_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__mult__le__cancel1_1) ).
cnf(cls_mult__le__cancel__left__neg_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_lessequals(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
cnf(cls_mult__le__cancel__left__neg_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
cnf(cls_mult__le__cancel__left__pos_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
cnf(cls_mult__le__cancel__left__pos_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
cnf(cls_mult__left__le__imp__le_0,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__left__le__imp__le_0) ).
cnf(cls_mult__right__le__imp__le_0,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__right__le__imp__le_0) ).
cnf(cls_one__less__mult_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_one__less__mult_0) ).
cnf(cls_inj__on__empty_0,axiom,
c_Fun_Oinj__on(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b),
file('theBenchmark.p',cls_inj__on__empty_0) ).
cnf(cls_zero__less__Suc_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat),
file('theBenchmark.p',cls_zero__less__Suc_0) ).
cnf(cls_gr0__conv__Suc_1,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat),
file('theBenchmark.p',cls_gr0__conv__Suc_1) ).
cnf(cls_Int__commute_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__commute_0) ).
cnf(cls_inf__commute_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__commute_0) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
cnf(cls_left__add__mult__distrib_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_k,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_u,tc_nat),V_k,tc_nat),
file('theBenchmark.p',cls_left__add__mult__distrib_0) ).
cnf(cls_combine__common__factor_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a)
| ~ class_Ring__and__Field_Osemiring(T_a) ),
file('theBenchmark.p',cls_combine__common__factor_0) ).
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_insert__Diff__single_0,axiom,
c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,V_A,T_a),
file('theBenchmark.p',cls_insert__Diff__single_0) ).
cnf(cls_nat__0__less__mult__iff_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
cnf(cls_nat__0__less__mult__iff_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ),
file('theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
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(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),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_dvd__0__left_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__0__left_0) ).
cnf(cls_sum__squares__le__zero__iff_0,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
cnf(cls_sum__squares__le__zero__iff_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
cnf(cls_dvd__imp__mod__0_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Divides_Odiv__class_Omod(V_b,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__imp__mod__0_0) ).
cnf(cls_dvd__eq__mod__eq__0_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Divides_Odiv__class_Omod(V_b,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
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),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),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),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__pos__nonneg_0) ).
cnf(cls_mult__le__0__iff_4,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__0__iff_4) ).
cnf(cls_mult__le__0__iff_5,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__0__iff_5) ).
cnf(cls_split__mult__neg__le_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('theBenchmark.p',cls_split__mult__neg__le_0) ).
cnf(cls_split__mult__neg__le_1,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('theBenchmark.p',cls_split__mult__neg__le_1) ).
cnf(cls_mult__nonneg__nonpos_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
cnf(cls_mult__nonpos__nonneg_0,axiom,
( ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
cnf(cls_mult__nonneg__nonpos2_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
cnf(cls_not__square__less__zero_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_not__square__less__zero_0) ).
cnf(cls_image__set__diff_0,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(V_f,V_A,T_a,T_b),c_Set_Oimage(V_f,V_B,T_a,T_b),tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_image__set__diff_0) ).
cnf(cls_Suc__mult__less__cancel1_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
cnf(cls_Suc__mult__less__cancel1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).
cnf(cls_nat__dvd__1__iff__1_1,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('theBenchmark.p',cls_nat__dvd__1__iff__1_1) ).
cnf(cls_natgb_Oadd__cancel_0,axiom,
( V_y = V_z
| c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat) != c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat) ),
file('theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
cnf(cls_nat__add__right__cancel_0,axiom,
( V_m = V_n
| c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat) != c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat) ),
file('theBenchmark.p',cls_nat__add__right__cancel_0) ).
cnf(cls_nat__add__left__cancel_0,axiom,
( V_m = V_n
| c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__add__left__cancel_0) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( V_y = V_z
| c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a)
| ~ 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
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
| ~ 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
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
| ~ 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
| c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
| ~ class_OrderedGroup_Ocancel__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__right__cancel_0) ).
cnf(cls_mult__right__le__one__le_0,axiom,
( ~ 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)
| ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_x,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_mult__right__le__one__le_0) ).
cnf(cls_mult__left__le__one__le_0,axiom,
( ~ 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)
| ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),V_x,T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('theBenchmark.p',cls_mult__left__le__one__le_0) ).
cnf(cls_mod__Suc_0,axiom,
( c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) != V_n ),
file('theBenchmark.p',cls_mod__Suc_0) ).
cnf(cls_mod__mult__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__left__eq_0) ).
cnf(cls_mod__mult__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__right__eq_0) ).
cnf(cls_add__is__1_3,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_add__is__1_3) ).
cnf(cls_add__is__1_0,axiom,
( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_add__is__1_0) ).
cnf(cls_sum__squares__gt__zero__iff_1,axiom,
( V_x = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
cnf(cls_sum__squares__gt__zero__iff_2,axiom,
( V_y = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_psubset__insert__iff_9,axiom,
( ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_psubset__insert__iff_9) ).
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_dvd__add_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__add_0) ).
cnf(cls_inv__image__comp_0,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),c_Set_Oimage(V_f,V_X,T_a,T_b),T_b,T_a) = V_X ),
file('theBenchmark.p',cls_inv__image__comp_0) ).
cnf(cls_image__inv__f__f_0,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b,T_a) = V_A ),
file('theBenchmark.p',cls_image__inv__f__f_0) ).
cnf(cls_Diff__disjoint_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__disjoint_0) ).
cnf(cls_dvd__1__iff__1_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_dvd__1__iff__1_0) ).
cnf(cls_mult__less__cancel__left__disj_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
cnf(cls_mult__less__cancel__left__disj_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
cnf(cls_mult__less__cancel__right__disj_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
cnf(cls_mult__less__cancel__right__disj_3,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
cnf(cls_nat__mult__eq__1__iff_2,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
file('theBenchmark.p',cls_nat__mult__eq__1__iff_2) ).
cnf(cls_card__gt__0__iff_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_nat),
file('theBenchmark.p',cls_card__gt__0__iff_0) ).
cnf(cls_full__nat__induct_1,axiom,
( ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(V_P)))
| hBOOL(hAPP(V_P,V_n)) ),
file('theBenchmark.p',cls_full__nat__induct_1) ).
cnf(cls_mod__mult__distrib2_0,axiom,
c_HOL_Otimes__class_Otimes(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat),
file('theBenchmark.p',cls_mod__mult__distrib2_0) ).
cnf(cls_mod__mult__distrib_0,axiom,
c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_k,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat),
file('theBenchmark.p',cls_mod__mult__distrib_0) ).
cnf(cls_mult__less__cancel2_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__less__cancel2_2) ).
cnf(cls_mult__less__cancel1_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__less__cancel1_2) ).
cnf(cls_mult__less__mono2_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__less__mono2_0) ).
cnf(cls_mult__less__mono1_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__less__mono1_0) ).
cnf(cls_nat__mult__less__cancel1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__mult__less__cancel1_0) ).
cnf(cls_nat__mult__less__cancel1_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__mult__less__cancel1_1) ).
cnf(cls_mult__less__cancel__left__neg_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
cnf(cls_mult__less__cancel__left__neg_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
cnf(cls_mult__less__cancel__left__pos_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
cnf(cls_mult__less__cancel__left__pos_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
cnf(cls_mult__strict__left__mono__neg_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
cnf(cls_mult__strict__left__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__strict__left__mono_0) ).
cnf(cls_mult__less__cancel__left__disj_4,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
cnf(cls_mult__less__cancel__left__disj_5,axiom,
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
cnf(cls_mult__strict__right__mono__neg_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
cnf(cls_mult__strict__right__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__strict__right__mono_0) ).
cnf(cls_mult__less__cancel__right__disj_4,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
cnf(cls_mult__less__cancel__right__disj_5,axiom,
( ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
cnf(cls_mult__strict__left__mono__comm_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
cnf(cls_less__add__iff2_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_less__add__iff2_0) ).
cnf(cls_less__add__iff1_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_less__add__iff1_1) ).
cnf(cls_less__add__iff1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_less__add__iff1_0) ).
cnf(cls_card__eq__SucD_3,axiom,
( c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(V_A,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| c_Finite__Set_Ocard(V_A,T_a) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_card__eq__SucD_3) ).
cnf(cls_mult__eq__0__iff_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) ),
file('theBenchmark.p',cls_mult__eq__0__iff_0) ).
cnf(cls_no__zero__divisors_0,axiom,
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ),
file('theBenchmark.p',cls_no__zero__divisors_0) ).
cnf(cls_no__zero__divirors__neq0_0,axiom,
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a) ),
file('theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
cnf(cls_mult__is__0_0,axiom,
( V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_mult__is__0_0) ).
cnf(cls_fun__upd__twist_0,axiom,
( V_a = V_c
| c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_m,V_a,V_b,T_a,T_b),V_c,V_d,T_a,T_b) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_m,V_c,V_d,T_a,T_b),V_a,V_b,T_a,T_b) ),
file('theBenchmark.p',cls_fun__upd__twist_0) ).
cnf(cls_not__psubset__empty_0,axiom,
~ c_HOL_Oord__class_Oless(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_not__psubset__empty_0) ).
cnf(cls_mod__add__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a_H,V_b_H,T_a),V_c,T_a)
| c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__cong_0) ).
cnf(cls_less__Suc0_1,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('theBenchmark.p',cls_less__Suc0_1) ).
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(c_HOL_Oplus__class_Oplus(V_a,V_a,T_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(c_HOL_Oplus__class_Oplus(V_a,V_a,T_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_even__less__0__iff_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_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(c_HOL_Oplus__class_Oplus(V_a,V_a,T_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_one__is__add_1,axiom,
( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_one__is__add_1) ).
cnf(cls_one__is__add_2,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_one__is__add_2) ).
cnf(cls_zero__less__mult__pos2_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a)
| ~ 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)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_zero__less__mult__pos2_0) ).
cnf(cls_zero__less__mult__pos_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ 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)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_zero__less__mult__pos_0) ).
cnf(cls_mult__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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__pos__pos_0) ).
cnf(cls_mult__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(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__neg__neg_0) ).
cnf(cls_nat__0__less__mult__iff_2,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),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
cnf(cls_injD_0,axiom,
( V_x = V_y
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| hAPP(V_f,V_x) != hAPP(V_f,V_y) ),
file('theBenchmark.p',cls_injD_0) ).
cnf(cls_mult__Suc__right_0,axiom,
c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat),
file('theBenchmark.p',cls_mult__Suc__right_0) ).
cnf(cls_mult__Suc_0,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat),
file('theBenchmark.p',cls_mult__Suc_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_inf__sup__aci_I2_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
cnf(cls_inf__sup__aci_I3_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
cnf(cls_inf__left__commute_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__left__commute_0) ).
cnf(cls_inf__assoc_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__assoc_0) ).
cnf(cls_Int__assoc_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__assoc_0) ).
cnf(cls_Int__left__commute_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__left__commute_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_finite__UNIV__card__ge__0_0,axiom,
( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a),tc_nat) ),
file('theBenchmark.p',cls_finite__UNIV__card__ge__0_0) ).
cnf(cls_not__sum__squares__lt__zero_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
cnf(cls_dvd__1__iff__1_1,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('theBenchmark.p',cls_dvd__1__iff__1_1) ).
cnf(cls_of__nat__mult_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a) = c_HOL_Otimes__class_Otimes(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_Osemiring__1(T_a) ),
file('theBenchmark.p',cls_of__nat__mult_0) ).
cnf(cls_mod__mult__self4_0,axiom,
c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat)),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat),
file('theBenchmark.p',cls_mod__mult__self4_0) ).
cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
( V_w = V_x
| V_y = V_z
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
( V_a = V_b
| V_c = V_d
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
cnf(cls_natgb_Onoteq__reduce_0,axiom,
( V_a = V_b
| V_c = V_d
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_d,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).
cnf(cls_natgb_Oadd__mul__solve_0,axiom,
( V_w = V_x
| V_y = V_z
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).
cnf(cls_Min__singleton_0,axiom,
( c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_Min__singleton_0) ).
cnf(cls_empty__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_empty__Diff_0) ).
cnf(cls_inj__image__eq__iff_0,axiom,
( V_A = V_B
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| c_Set_Oimage(V_f,V_A,T_a,T_b) != c_Set_Oimage(V_f,V_B,T_a,T_b) ),
file('theBenchmark.p',cls_inj__image__eq__iff_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(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),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__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(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),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_mult__eq__self__implies__10_0,axiom,
( V_n = c_HOL_Oone__class_Oone(tc_nat)
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| V_m != c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_mult__eq__self__implies__10_0) ).
cnf(cls_sum__squares__le__zero__iff_2,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
cnf(cls_inf__eq__top__eq2_0,axiom,
( V_B = c_Orderings_Otop__class_Otop(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,T_a) != c_Orderings_Otop__class_Otop(T_a)
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_inf__eq__top__eq2_0) ).
cnf(cls_inf__eq__top__eq1_0,axiom,
( V_A = c_Orderings_Otop__class_Otop(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,T_a) != c_Orderings_Otop__class_Otop(T_a)
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_inf__eq__top__eq1_0) ).
cnf(cls_mod__mult__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a_H,V_b_H,T_a),V_c,T_a)
| c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__cong_0) ).
cnf(cls_dvd__0__right_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__0__right_0) ).
cnf(cls_mult__eq__1__iff_2,axiom,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('theBenchmark.p',cls_mult__eq__1__iff_2) ).
cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
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_class__semiring_Osemiring__rules_I9_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
cnf(cls_mult__eq__0__iff_2,axiom,
( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) ),
file('theBenchmark.p',cls_mult__eq__0__iff_2) ).
cnf(cls_mult__eq__0__iff_1,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a) ),
file('theBenchmark.p',cls_mult__eq__0__iff_1) ).
cnf(cls_mult__zero__right_0,axiom,
( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) ),
file('theBenchmark.p',cls_mult__zero__right_0) ).
cnf(cls_mult__zero__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a) ),
file('theBenchmark.p',cls_mult__zero__left_0) ).
cnf(cls_mult__is__0_1,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_mult__is__0_1) ).
cnf(cls_mult__is__0_2,axiom,
c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_mult__is__0_2) ).
cnf(cls_class__semiring_Omul__0_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Omul__0_0) ).
cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),V_m,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
file('theBenchmark.p',cls_bot1E_0) ).
cnf(cls_Diff__Int__distrib_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_C,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__Int__distrib_0) ).
cnf(cls_Diff__Int__distrib2_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__Int__distrib2_0) ).
cnf(cls_mod__1_0,axiom,
c_Divides_Odiv__class_Omod(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_mod__1_0) ).
cnf(cls_UNIV__not__empty_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_UNIV__not__empty_0) ).
cnf(cls_add__eq__if_1,axiom,
( V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_n,tc_nat)) ),
file('theBenchmark.p',cls_add__eq__if_1) ).
cnf(cls_inc__induct_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ hBOOL(hAPP(V_P,V_j))
| c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(V_P,V_j),V_j,tc_nat)
| hBOOL(hAPP(V_P,V_i)) ),
file('theBenchmark.p',cls_inc__induct_0) ).
cnf(cls_fun__upd__upd_0,axiom,
c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_x,V_z,T_a,T_b) = c_Fun_Ofun__upd(V_f,V_x,V_z,T_a,T_b),
file('theBenchmark.p',cls_fun__upd__upd_0) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_x,V_B,T_a) ),
file('theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
cnf(cls_mod__by__1_0,axiom,
( c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__by__1_0) ).
cnf(cls_inf__top__right_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Orderings_Otop__class_Otop(T_a),T_a) = V_x
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_inf__top__right_0) ).
cnf(cls_inf__top__left_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(T_a),V_x,T_a) = V_x
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_inf__top__left_0) ).
cnf(cls_Int__UNIV__left_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B,
file('theBenchmark.p',cls_Int__UNIV__left_0) ).
cnf(cls_Int__UNIV__right_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A,
file('theBenchmark.p',cls_Int__UNIV__right_0) ).
cnf(cls_image__vimage__eq_0,axiom,
c_Set_Oimage(V_f,c_Set_Ovimage(V_f,V_A,T_b,T_a),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_image__vimage__eq_0) ).
cnf(cls_dvd__reduce_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_dvd__reduce_0) ).
cnf(cls_dvd__reduce_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_dvd__reduce_1) ).
cnf(cls_Diff__Int2_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__Int2_0) ).
cnf(cls_mod__if_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = V_m ),
file('theBenchmark.p',cls_mod__if_0) ).
cnf(cls_one__is__add_4,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_one__is__add_4) ).
cnf(cls_psubset__eq_1,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_psubset__eq_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_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_x)),
file('theBenchmark.p',cls_top1I_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),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('theBenchmark.p',cls_add__pos__pos_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_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_card__empty_0,axiom,
c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_card__empty_0) ).
cnf(cls_card__gt__0__iff_2,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ),
file('theBenchmark.p',cls_card__gt__0__iff_2) ).
cnf(cls_mult__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
file('theBenchmark.p',cls_mult__mono_0) ).
cnf(cls_mult__mono_H_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
file('theBenchmark.p',cls_mult__mono_H_0) ).
cnf(cls_zero__less__two_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_zero__less__two_0) ).
cnf(cls_inf1E_1,axiom,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
| hBOOL(hAPP(V_B,V_x)) ),
file('theBenchmark.p',cls_inf1E_1) ).
cnf(cls_inf1E_0,axiom,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
| hBOOL(hAPP(V_A,V_x)) ),
file('theBenchmark.p',cls_inf1E_0) ).
cnf(cls_mod__mult__self3_0,axiom,
c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat),V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),
file('theBenchmark.p',cls_mod__mult__self3_0) ).
cnf(cls_mod__mult__self1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__self1_0) ).
cnf(cls_mod__mult__self2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__self2_0) ).
cnf(cls_fun__upd__idem__iff_0,axiom,
( hAPP(V_f,V_x) = V_y
| c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b) != V_f ),
file('theBenchmark.p',cls_fun__upd__idem__iff_0) ).
cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
cnf(cls_nat__mult__dvd__cancel__disj_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
| V_k = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__mult__dvd__cancel__disj_0) ).
cnf(cls_dvd__mult__cancel__left_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
cnf(cls_dvd__mult__cancel__right_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_dvd__mult__cancel__right_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_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_vimage__subsetI_0,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool))
| c_lessequals(c_Set_Ovimage(V_f,V_B,T_a,T_b),V_A,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_vimage__subsetI_0) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = 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,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
cnf(cls_natgb_Oadd__r0__iff_1,axiom,
V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
cnf(cls_plus__nat_Oadd__0_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n,
file('theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
cnf(cls_Nat_Oadd__0__right_0,axiom,
c_HOL_Oplus__class_Oplus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m,
file('theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
( V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),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,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),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,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_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,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),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,
( c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),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,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_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_sum__squares__gt__zero__iff_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
cnf(cls_zero__le__mult__iff_0,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_zero__le__mult__iff_0) ).
cnf(cls_zero__le__mult__iff_1,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_zero__le__mult__iff_1) ).
cnf(cls_zero__le__mult__iff_2,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_zero__le__mult__iff_2) ).
cnf(cls_zero__le__mult__iff_3,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_zero__le__mult__iff_3) ).
cnf(cls_less__1__mult_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_m,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_n,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(V_m,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_less__1__mult_0) ).
cnf(cls_split__mod_1,axiom,
( hBOOL(hAPP(V_P,V_j))
| ~ hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),V_j,tc_nat),V_k,tc_nat)))
| V_k = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat) ),
file('theBenchmark.p',cls_split__mod_1) ).
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(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),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(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__less__le__mono_0) ).
cnf(cls_vimage__Int_0,axiom,
c_Set_Ovimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_vimage__Int_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),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),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),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),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),c_HOL_Oplus__class_Oplus(V_a,V_a,T_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),c_HOL_Oplus__class_Oplus(V_a,V_a,T_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_dvd_Oless__le__trans_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat) ),
file('theBenchmark.p',cls_dvd_Oless__le__trans_1) ).
cnf(cls_dvd_Ole__less__trans_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat) ),
file('theBenchmark.p',cls_dvd_Ole__less__trans_1) ).
cnf(cls_Int__iff_2,axiom,
( ~ c_in(V_c,V_A,T_a)
| ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_Int__iff_2) ).
cnf(cls_IntI_0,axiom,
( ~ c_in(V_c,V_A,T_a)
| ~ c_in(V_c,V_B,T_a)
| c_in(V_c,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_IntI_0) ).
cnf(cls_ex__in__conv_0,axiom,
~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_ex__in__conv_0) ).
cnf(cls_ball__empty_0,axiom,
( ~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_ball__empty_0) ).
cnf(cls_empty__iff_0,axiom,
~ c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_empty__iff_0) ).
cnf(cls_emptyE_0,axiom,
~ c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_emptyE_0) ).
cnf(cls_UNIV__I_0,axiom,
c_in(V_x,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_UNIV__I_0) ).
cnf(cls_DiffE_1,axiom,
( ~ c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| ~ c_in(V_c,V_B,T_a) ),
file('theBenchmark.p',cls_DiffE_1) ).
cnf(cls_DiffE_0,axiom,
( ~ c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| c_in(V_c,V_A,T_a) ),
file('theBenchmark.p',cls_DiffE_0) ).
cnf(cls_psubsetD_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ),
file('theBenchmark.p',cls_psubsetD_0) ).
cnf(cls_IntE_1,axiom,
( ~ c_in(V_c,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| c_in(V_c,V_B,T_a) ),
file('theBenchmark.p',cls_IntE_1) ).
cnf(cls_IntE_0,axiom,
( ~ c_in(V_c,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| c_in(V_c,V_A,T_a) ),
file('theBenchmark.p',cls_IntE_0) ).
cnf(cls_inj__on__contraD_0,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| V_x = V_y
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_y,V_A,T_a)
| hAPP(V_f,V_x) != hAPP(V_f,V_y) ),
file('theBenchmark.p',cls_inj__on__contraD_0) ).
cnf(cls_inj__on__iff_0,axiom,
( V_x = V_y
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_y,V_A,T_a)
| hAPP(V_f,V_x) != hAPP(V_f,V_y) ),
file('theBenchmark.p',cls_inj__on__iff_0) ).
cnf(cls_inj__on__def_0,axiom,
( V_x = V_xa
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_xa,V_A,T_a)
| hAPP(V_f,V_x) != hAPP(V_f,V_xa) ),
file('theBenchmark.p',cls_inj__on__def_0) ).
cnf(cls_inj__onD_0,axiom,
( ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_y,V_A,T_a)
| V_x = V_y
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| hAPP(V_f,V_x) != hAPP(V_f,V_y) ),
file('theBenchmark.p',cls_inj__onD_0) ).
cnf(cls_bex__empty_0,axiom,
( ~ c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| ~ hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_bex__empty_0) ).
cnf(cls_Diff__iff_2,axiom,
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a)
| c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_Diff__iff_2) ).
cnf(cls_DiffI_0,axiom,
( ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a)
| c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_DiffI_0) ).
cnf(cls_vimage__eq_1,axiom,
( ~ c_in(hAPP(V_f,V_a),V_B,T_b)
| c_in(V_a,c_Set_Ovimage(V_f,V_B,T_a,T_b),T_a) ),
file('theBenchmark.p',cls_vimage__eq_1) ).
cnf(cls_vimageI2_0,axiom,
( ~ c_in(hAPP(V_f,V_a),V_A,T_a)
| c_in(V_a,c_Set_Ovimage(V_f,V_A,T_b,T_a),T_b) ),
file('theBenchmark.p',cls_vimageI2_0) ).
cnf(cls_vimageI_0,axiom,
( ~ c_in(hAPP(V_f,V_a),V_B,T_a)
| c_in(V_a,c_Set_Ovimage(V_f,V_B,T_b,T_a),T_b) ),
file('theBenchmark.p',cls_vimageI_0) ).
cnf(cls_vimageE_0,axiom,
( ~ c_in(V_a,c_Set_Ovimage(V_f,V_B,T_a,T_b),T_a)
| c_in(hAPP(V_f,V_a),V_B,T_b) ),
file('theBenchmark.p',cls_vimageE_0) ).
cnf(cls_vimageD_0,axiom,
( ~ c_in(V_a,c_Set_Ovimage(V_f,V_A,T_a,T_b),T_a)
| c_in(hAPP(V_f,V_a),V_A,T_b) ),
file('theBenchmark.p',cls_vimageD_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,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),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_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_gfp__upperbound_0,axiom,
( ~ c_lessequals(V_X,hAPP(V_f,V_X),T_a)
| c_lessequals(V_X,c_Inductive_Ocomplete__lattice__class_Ogfp(V_f,T_a),T_a)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_gfp__upperbound_0) ).
cnf(cls_top__greatest_0,axiom,
( c_lessequals(V_x,c_Orderings_Otop__class_Otop(T_a),T_a)
| ~ class_Orderings_Otop(T_a) ),
file('theBenchmark.p',cls_top__greatest_0) ).
cnf(cls_inf__le1_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__le1_0) ).
cnf(cls_inf__le2_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__le2_0) ).
cnf(cls_le__infI_0,axiom,
( ~ c_lessequals(V_x,V_a,T_a)
| ~ c_lessequals(V_x,V_b,T_a)
| c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__infI_0) ).
cnf(cls_le__inf__iff_2,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_z,T_a)
| c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__inf__iff_2) ).
cnf(cls_inf__greatest_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_z,T_a)
| c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__greatest_0) ).
cnf(cls_inf__sup__ord_I2_J_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
cnf(cls_add__left__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),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(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),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(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),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(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),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(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),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(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),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_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_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_dvd_Oeq__iff_2,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
| V_x = V_y ),
file('theBenchmark.p',cls_dvd_Oeq__iff_2) ).
cnf(cls_dvd_Oantisym_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
| V_x = V_y ),
file('theBenchmark.p',cls_dvd_Oantisym_0) ).
cnf(cls_dvd_Oless__le_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
| V_x = V_y
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat) ),
file('theBenchmark.p',cls_dvd_Oless__le_0) ).
cnf(cls_dvd__antisym_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat)
| V_m = V_n ),
file('theBenchmark.p',cls_dvd__antisym_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_dvd_Oantisym__conv_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
| V_x = V_y ),
file('theBenchmark.p',cls_dvd_Oantisym__conv_0) ).
cnf(cls_dvd_Ole__neq__trans_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat)
| V_a = V_b
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat) ),
file('theBenchmark.p',cls_dvd_Ole__neq__trans_0) ).
cnf(cls_dvd_Oneq__le__trans_0,axiom,
( V_a = V_b
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat) ),
file('theBenchmark.p',cls_dvd_Oneq__le__trans_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_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_nat__dvd__not__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat) ),
file('theBenchmark.p',cls_nat__dvd__not__less_0) ).
cnf(cls_Suc__diff__1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = V_n ),
file('theBenchmark.p',cls_Suc__diff__1_0) ).
cnf(cls_Suc__pred_H_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| V_n = c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
file('theBenchmark.p',cls_Suc__pred_H_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(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),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(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_add__less__mono_0) ).
cnf(cls_less__infI2_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_less__infI2_0) ).
cnf(cls_less__infI1_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_less__infI1_0) ).
cnf(cls_dvd__trans_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__trans_0) ).
cnf(cls_dvd__refl_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__refl_0) ).
cnf(cls_dvd_Oeq__iff_0,axiom,
c_Ring__and__Field_Odvd__class_Odvd(V_x,V_x,tc_nat),
file('theBenchmark.p',cls_dvd_Oeq__iff_0) ).
cnf(cls_dvd_Oless__trans_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) ),
file('theBenchmark.p',cls_dvd_Oless__trans_0) ).
cnf(cls_dvd_Oorder__trans_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) ),
file('theBenchmark.p',cls_dvd_Oorder__trans_0) ).
cnf(cls_less__iff__diff__less__0_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_less__iff__diff__less__0_1) ).
cnf(cls_less__iff__diff__less__0_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_less__iff__diff__less__0_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_dvd__mult__cancel__right_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
cnf(cls_dvd__mult__cancel__left_1,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
cnf(cls_nat__mult__dvd__cancel__disj_1,axiom,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat),
file('theBenchmark.p',cls_nat__mult__dvd__cancel__disj_1) ).
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_atLeast__eq__iff_0,axiom,
( V_x = V_y
| c_SetInterval_Oord__class_OatLeast(V_x,T_a) != c_SetInterval_Oord__class_OatLeast(V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_atLeast__eq__iff_0) ).
cnf(cls_mult__less__cancel1_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_mult__less__cancel1_1) ).
cnf(cls_mult__less__cancel2_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_mult__less__cancel2_1) ).
cnf(cls_fun__upd__idem_0,axiom,
c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_b,T_a) = V_f,
file('theBenchmark.p',cls_fun__upd__idem_0) ).
cnf(cls_fun__upd__same_0,axiom,
hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_x) = V_y,
file('theBenchmark.p',cls_fun__upd__same_0) ).
cnf(cls_fun__upd__triv_0,axiom,
c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_a,T_b) = V_f,
file('theBenchmark.p',cls_fun__upd__triv_0) ).
cnf(cls_fun__upd__apply_0,axiom,
hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_aa),V_x) = V_y,
file('theBenchmark.p',cls_fun__upd__apply_0) ).
cnf(cls_fun__upd__idem__iff_1,axiom,
c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_aa,T_a) = V_f,
file('theBenchmark.p',cls_fun__upd__idem__iff_1) ).
cnf(cls_nat__mult__dvd__cancel1_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__mult__dvd__cancel1_1) ).
cnf(cls_nat__mult__dvd__cancel1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__mult__dvd__cancel1_0) ).
cnf(cls_dvd__mult__cancel_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_dvd__mult__cancel_0) ).
cnf(cls_less__add__one_0,axiom,
( c_HOL_Oord__class_Oless(V_a,c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_less__add__one_0) ).
cnf(cls_mult__left__idem_0,axiom,
( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) ),
file('theBenchmark.p',cls_mult__left__idem_0) ).
cnf(cls_nat__mod__eq__iff_1,axiom,
( c_Divides_Odiv__class_Omod(V_x,V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_y,V_n,tc_nat)
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_n,V_xa,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(V_y,c_HOL_Otimes__class_Otimes(V_n,V_xb,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__mod__eq__iff_1) ).
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_mult__less__le__imp__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(V_c,V_d,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(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__le__imp__less_0) ).
cnf(cls_mult__le__less__imp__less_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(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__less__imp__less_0) ).
cnf(cls_one__dvd_0,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_one__dvd_0) ).
cnf(cls_Diff__UNIV_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__UNIV_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_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_mod__add__self2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__self2_0) ).
cnf(cls_mod__add__self1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__add__self1_0) ).
cnf(cls_mult__le__0__iff_3,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__0__iff_3) ).
cnf(cls_mult__le__0__iff_2,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__0__iff_2) ).
cnf(cls_mult__le__0__iff_1,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| 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)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__0__iff_1) ).
cnf(cls_mult__le__0__iff_0,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__le__0__iff_0) ).
cnf(cls_mult__pos__neg2_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,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__pos__neg2_0) ).
cnf(cls_mult__pos__neg_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,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__pos__neg_0) ).
cnf(cls_mult__neg__pos_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_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_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__neg__pos_0) ).
cnf(cls_n__less__m__mult__n_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)
| c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_n__less__m__mult__n_0) ).
cnf(cls_n__less__n__mult__m_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)
| c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_n__less__n__mult__m_0) ).
cnf(cls_dvd__mult__right_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__mult__right_0) ).
cnf(cls_dvd__mult__left_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__mult__left_0) ).
cnf(cls_dvd__mult2_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__mult2_0) ).
cnf(cls_dvd__mult_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_dvd__mult_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,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_pos__add__strict_0) ).
cnf(cls_inf__sup__aci_I4_J_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
cnf(cls_inf__left__idem_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__left__idem_0) ).
cnf(cls_Int__left__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__left__absorb_0) ).
cnf(cls_mod__mod__cancel_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_b,T_a)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(V_a,V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mod__cancel_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(c_HOL_Oplus__class_Oplus(V_a,V_a,T_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_double__add__le__zero__iff__single__add__le__zero_0,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_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_mult__cancel1_1,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),
file('theBenchmark.p',cls_mult__cancel1_1) ).
cnf(cls_mult__cancel2_1,axiom,
c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_mult__cancel2_1) ).
cnf(cls_not__add__less1_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat),
file('theBenchmark.p',cls_not__add__less1_0) ).
cnf(cls_not__add__less2_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat),
file('theBenchmark.p',cls_not__add__less2_0) ).
cnf(cls_mult__dvd__mono_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_mult__dvd__mono_0) ).
cnf(cls_mod__lemma_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_c,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_r,V_b,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(V_q,V_c,tc_nat),tc_nat),V_r,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mod__lemma_0) ).
cnf(cls_mult__right__mono__neg_0,axiom,
( ~ c_lessequals(V_b,V_a,T_a)
| ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_mult__right__mono__neg_0) ).
cnf(cls_mult__left__mono__neg_0,axiom,
( ~ c_lessequals(V_b,V_a,T_a)
| ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_mult__left__mono__neg_0) ).
cnf(cls_mult__right__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Omult__mono(T_a) ),
file('theBenchmark.p',cls_mult__right__mono_0) ).
cnf(cls_mult__left__mono_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Omult__mono(T_a) ),
file('theBenchmark.p',cls_mult__left__mono_0) ).
cnf(cls_mult__mono1_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Omult__mono1(T_a) ),
file('theBenchmark.p',cls_mult__mono1_0) ).
cnf(cls_mod__if_1,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_mod__if_1) ).
cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom,
( V_r = c_HOL_Ozero__class_Ozero(T_a)
| V_c = V_d
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,T_a),T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ),
file('theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
cnf(cls_natgb_Oadd__scale__eq__noteq_0,axiom,
( V_r = c_HOL_Ozero__class_Ozero(tc_nat)
| V_c = V_d
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).
cnf(cls_sum__squares__eq__zero__iff_1,axiom,
( V_y = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
cnf(cls_sum__squares__eq__zero__iff_0,axiom,
( V_x = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
cnf(cls_less__diff__conv_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) ),
file('theBenchmark.p',cls_less__diff__conv_0) ).
cnf(cls_less__diff__conv_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)
| c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_less__diff__conv_1) ).
cnf(cls_inf__idem_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,V_x,T_a) = V_x
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__idem_0) ).
cnf(cls_Int__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A,
file('theBenchmark.p',cls_Int__absorb_0) ).
cnf(cls_add__strict__right__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),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(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('theBenchmark.p',cls_add__less__cancel__right_1) ).
cnf(cls_bot__least_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(T_a),V_x,T_a)
| ~ class_Orderings_Obot(T_a) ),
file('theBenchmark.p',cls_bot__least_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(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a) ),
file('theBenchmark.p',cls_add__mono_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_le__iff__inf_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_x
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__iff__inf_0) ).
cnf(cls_le__iff__inf_1,axiom,
( c_lessequals(V_x,V_y,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__iff__inf_1) ).
cnf(cls_inf__absorb2_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_inf__absorb2_0) ).
cnf(cls_le__infE_0,axiom,
( ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a)
| c_lessequals(V_x,V_a,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__infE_0) ).
cnf(cls_le__infE_1,axiom,
( ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a)
| c_lessequals(V_x,V_b,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__infE_1) ).
cnf(cls_le__infI1_0,axiom,
( ~ c_lessequals(V_a,V_x,T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__infI1_0) ).
cnf(cls_le__infI2_0,axiom,
( ~ c_lessequals(V_b,V_x,T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__infI2_0) ).
cnf(cls_le__inf__iff_0,axiom,
( ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__inf__iff_0) ).
cnf(cls_le__inf__iff_1,axiom,
( ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ class_Lattices_Olower__semilattice(T_a) ),
file('theBenchmark.p',cls_le__inf__iff_1) ).
cnf(cls_le__add__iff1_0,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_le__add__iff1_0) ).
cnf(cls_le__add__iff1_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_le__add__iff1_1) ).
cnf(cls_le__add__iff2_0,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_le__add__iff2_0) ).
cnf(cls_le__add__iff2_1,axiom,
( ~ c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_le__add__iff2_1) ).
cnf(cls_Min__in_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| c_in(c_Finite__Set_Olinorder__class_OMin(V_A,T_a),V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_Min__in_0) ).
cnf(cls_Max__in_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| c_in(c_Finite__Set_Olinorder__class_OMax(V_A,T_a),V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_Max__in_0) ).
cnf(cls_less__eqI_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_less__eqI_1) ).
cnf(cls_less__eqI_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_less__eqI_0) ).
cnf(cls_mod__diff__cong_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a_H,V_b_H,T_a),V_c,T_a)
| c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_mod__diff__cong_0) ).
cnf(cls_dvd__diff_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__ring__1(T_a) ),
file('theBenchmark.p',cls_dvd__diff_0) ).
cnf(cls_class__ringb_Osubr0__iff_1,axiom,
( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = 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_Osubr0__iff_1) ).
cnf(cls_diff__self_0,axiom,
( c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_diff__self_0) ).
cnf(cls_diff__0__right_0,axiom,
( c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_diff__0__right_0) ).
cnf(cls_right__minus__eq_1,axiom,
( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_right__minus__eq_1) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
cnf(cls_diff__add__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(cls_mod__diff__left__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_mod__diff__left__eq_0) ).
cnf(cls_mod__diff__right__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_mod__diff__right__eq_0) ).
cnf(cls_class__ringb_Osubr0__iff_0,axiom,
( V_x = V_y
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != 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_Osubr0__iff_0) ).
cnf(cls_right__minus__eq_0,axiom,
( V_a = V_b
| c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_right__minus__eq_0) ).
cnf(cls_eq__iff__diff__eq__0_1,axiom,
( V_a = V_b
| c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
cnf(cls_mod__diff__eq_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)
| ~ class_Divides_Oring__div(T_a) ),
file('theBenchmark.p',cls_mod__diff__eq_0) ).
cnf(cls_add__diff__cancel_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a
| ~ class_OrderedGroup_Ogroup__add(T_a) ),
file('theBenchmark.p',cls_add__diff__cancel_0) ).
cnf(cls_insert__Diff_0,axiom,
( ~ c_in(V_a,V_A,T_a)
| c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A ),
file('theBenchmark.p',cls_insert__Diff_0) ).
cnf(cls_vimage__singleton__eq_0,axiom,
( ~ c_in(V_a,c_Set_Ovimage(V_f,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),T_a,T_b),T_a)
| hAPP(V_f,V_a) = V_b ),
file('theBenchmark.p',cls_vimage__singleton__eq_0) ).
cnf(cls_vimage__singleton__eq_1,axiom,
c_in(V_a,c_Set_Ovimage(V_f,c_Set_Oinsert(hAPP(V_f,V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_aa,T_a),T_aa),
file('theBenchmark.p',cls_vimage__singleton__eq_1) ).
cnf(cls_Diff__insert__absorb_0,axiom,
( c_in(V_x,V_A,T_a)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A ),
file('theBenchmark.p',cls_Diff__insert__absorb_0) ).
cnf(cls_finite__UNIV_0,axiom,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)
| ~ class_Finite__Set_Ofinite_Ofinite(T_a) ),
file('theBenchmark.p',cls_finite__UNIV_0) ).
cnf(cls_finite_OemptyI_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_finite_OemptyI_0) ).
cnf(cls_finite__Diff2_1,axiom,
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_finite__Diff2_1) ).
cnf(cls_finite__Diff2_0,axiom,
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ),
file('theBenchmark.p',cls_finite__Diff2_0) ).
cnf(cls_finite__Diff_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_finite__Diff_0) ).
cnf(cls_finite__Int_1,axiom,
( ~ c_Finite__Set_Ofinite(V_G,T_a)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(V_F,V_G,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_finite__Int_1) ).
cnf(cls_finite__Int_0,axiom,
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(V_F,V_G,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_finite__Int_0) ).
cnf(cls_inj__on__fun__updI_0,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| c_in(V_y,c_Set_Oimage(V_f,V_A,T_a,T_b),T_b)
| c_Fun_Oinj__on(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_A,T_a,T_b) ),
file('theBenchmark.p',cls_inj__on__fun__updI_0) ).
cnf(cls_inj__image__mem__iff_1,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| ~ c_in(V_a,V_A,T_a)
| c_in(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) ),
file('theBenchmark.p',cls_inj__image__mem__iff_1) ).
cnf(cls_inj__image__mem__iff_0,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| ~ c_in(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b)
| c_in(V_a,V_A,T_a) ),
file('theBenchmark.p',cls_inj__image__mem__iff_0) ).
cnf(cls_psubset__insert__iff_5,axiom,
( c_in(V_x,V_B,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_psubset__insert__iff_5) ).
cnf(cls_fun__upd__image_0,axiom,
( ~ c_in(V_x,V_A,T_b)
| c_Set_Oimage(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_A,T_b,T_a) = c_Set_Oinsert(V_y,c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),tc_fun(T_b,tc_bool)),T_b,T_a),T_a) ),
file('theBenchmark.p',cls_fun__upd__image_0) ).
cnf(cls_inj__on__insert_2,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| c_in(hAPP(V_f,V_a),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b),T_b)
| c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b) ),
file('theBenchmark.p',cls_inj__on__insert_2) ).
cnf(cls_inj__on__insert_1,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b)
| ~ c_in(hAPP(V_f,V_a),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b),T_b) ),
file('theBenchmark.p',cls_inj__on__insert_1) ).
cnf(cls_Suc__mult__cancel1_0,axiom,
( V_m = V_n
| c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__mult__cancel1_0) ).
cnf(cls_less__SucI_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ),
file('theBenchmark.p',cls_less__SucI_0) ).
cnf(cls_Suc__lessD_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__lessD_0) ).
cnf(cls_mod__Suc__eq__Suc__mod_0,axiom,
c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_n,tc_nat),
file('theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
cnf(cls_less__trans__Suc_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat) ),
file('theBenchmark.p',cls_less__trans__Suc_0) ).
cnf(cls_less__Suc__eq_2,axiom,
c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat),
file('theBenchmark.p',cls_less__Suc__eq_2) ).
cnf(cls_lessI_0,axiom,
c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat),
file('theBenchmark.p',cls_lessI_0) ).
cnf(cls_Suc__neq__Zero_0,axiom,
c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_Suc__neq__Zero_0) ).
cnf(cls_nat_Osimps_I3_J_0,axiom,
c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
cnf(cls_not__less__less__Suc__eq_0,axiom,
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| V_n = V_m ),
file('theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
cnf(cls_less__antisym_0,axiom,
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| V_m = V_n ),
file('theBenchmark.p',cls_less__antisym_0) ).
cnf(cls_less__SucE_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| V_m = V_n ),
file('theBenchmark.p',cls_less__SucE_0) ).
cnf(cls_Zero__neq__Suc_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m),
file('theBenchmark.p',cls_Zero__neq__Suc_0) ).
cnf(cls_nat_Osimps_I2_J_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H),
file('theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
cnf(cls_add__Suc_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)),
file('theBenchmark.p',cls_add__Suc_0) ).
cnf(cls_add__Suc__right_0,axiom,
c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)),
file('theBenchmark.p',cls_add__Suc__right_0) ).
cnf(cls_mod__Suc_1,axiom,
( c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) = V_n
| c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) ),
file('theBenchmark.p',cls_mod__Suc_1) ).
cnf(cls_add__Suc__shift_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat),
file('theBenchmark.p',cls_add__Suc__shift_0) ).
cnf(cls_Suc__lessI_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_Suc(V_m) = V_n
| c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__lessI_0) ).
cnf(cls_not__less__less__Suc__eq_1,axiom,
( c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat)
| c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ),
file('theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
cnf(cls_not__less__eq_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_not__less__eq_1) ).
cnf(cls_not__less__eq_0,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ),
file('theBenchmark.p',cls_not__less__eq_0) ).
cnf(cls_less__Suc__eq__0__disj_3,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat) ),
file('theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
cnf(cls_Suc__less__eq_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__less__eq_0) ).
cnf(cls_Suc__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ),
file('theBenchmark.p',cls_Suc__mono_0) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oinsert(V_a,V_A,T_a),
file('theBenchmark.p',cls_empty__not__insert_0) ).
cnf(cls_doubleton__eq__iff_3,axiom,
( V_b = V_d
| V_b = V_c
| c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ),
file('theBenchmark.p',cls_doubleton__eq__iff_3) ).
cnf(cls_doubleton__eq__iff_2,axiom,
( V_b = V_d
| V_a = V_d
| c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ),
file('theBenchmark.p',cls_doubleton__eq__iff_2) ).
cnf(cls_doubleton__eq__iff_1,axiom,
( V_a = V_c
| V_b = V_c
| c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ),
file('theBenchmark.p',cls_doubleton__eq__iff_1) ).
cnf(cls_doubleton__eq__iff_0,axiom,
( V_a = V_c
| V_a = V_d
| c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ),
file('theBenchmark.p',cls_doubleton__eq__iff_0) ).
cnf(cls_insert__inter__insert_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_A,T_a),c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_insert__inter__insert_0) ).
cnf(cls_insert__not__empty_0,axiom,
c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_insert__not__empty_0) ).
cnf(cls_inj__on__insert_0,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ),
file('theBenchmark.p',cls_inj__on__insert_0) ).
cnf(cls_doubleton__eq__iff_4,axiom,
c_Set_Oinsert(V_xa,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Set_Oinsert(V_x,c_Set_Oinsert(V_xa,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),
file('theBenchmark.p',cls_doubleton__eq__iff_4) ).
cnf(cls_singleton__inject_0,axiom,
( V_a = V_b
| c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) != c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_singleton__inject_0) ).
cnf(cls_subset__insert__iff_4,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insert__iff_4) ).
cnf(cls_less__fun__def_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_f,V_g,tc_fun(T_a,T_b))
| c_lessequals(V_f,V_g,tc_fun(T_a,T_b))
| ~ class_HOL_Oord(T_b) ),
file('theBenchmark.p',cls_less__fun__def_0) ).
cnf(cls_less__fun__def_2,axiom,
( ~ c_lessequals(V_f,V_g,tc_fun(T_a,T_b))
| c_lessequals(V_g,V_f,tc_fun(T_a,T_b))
| c_HOL_Oord__class_Oless(V_f,V_g,tc_fun(T_a,T_b))
| ~ class_HOL_Oord(T_b) ),
file('theBenchmark.p',cls_less__fun__def_2) ).
cnf(cls_less__fun__def_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_f,V_g,tc_fun(T_a,T_b))
| ~ c_lessequals(V_g,V_f,tc_fun(T_a,T_b))
| ~ class_HOL_Oord(T_b) ),
file('theBenchmark.p',cls_less__fun__def_1) ).
cnf(cls_subset__iff__psubset__eq_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| V_A = V_B ),
file('theBenchmark.p',cls_subset__iff__psubset__eq_0) ).
cnf(cls_add__less__cancel__right_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),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(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),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(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),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(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),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(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_add__less__mono1_0) ).
cnf(cls_nat__add__left__cancel__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),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(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
cnf(cls_split__mod_0,axiom,
( hBOOL(hAPP(V_P,V_n))
| ~ hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('theBenchmark.p',cls_split__mod_0) ).
cnf(cls_split__mod_5,axiom,
( hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(V_P,V_n)) ),
file('theBenchmark.p',cls_split__mod_5) ).
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(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),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_inv__f__f_0,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),hAPP(V_f,V_x)) = V_x ),
file('theBenchmark.p',cls_inv__f__f_0) ).
cnf(cls_inv__f__eq_0,axiom,
( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),V_f,T_aa,T_a),hAPP(V_f,V_x)) = V_x
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a) ),
file('theBenchmark.p',cls_inv__f__eq_0) ).
cnf(cls_nat__diff__split_0,axiom,
( ~ hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(V_a,V_b,tc_nat)))
| ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_nat)
| hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('theBenchmark.p',cls_nat__diff__split_0) ).
cnf(cls_add__is__1_5,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('theBenchmark.p',cls_add__is__1_5) ).
cnf(cls_Int__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__Diff_0) ).
cnf(cls_dvd__mult__cancel1_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_m,tc_nat)
| V_n = c_HOL_Oone__class_Oone(tc_nat) ),
file('theBenchmark.p',cls_dvd__mult__cancel1_0) ).
cnf(cls_dvd__mult__cancel2_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),V_m,tc_nat)
| V_n = c_HOL_Oone__class_Oone(tc_nat) ),
file('theBenchmark.p',cls_dvd__mult__cancel2_0) ).
cnf(cls_mult__idem_0,axiom,
( c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a) ),
file('theBenchmark.p',cls_mult__idem_0) ).
cnf(cls_mod__mult__self2__is__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
cnf(cls_mod__mult__self1__is__0_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
cnf(cls_mod__eq__0__iff_1,axiom,
c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_d,V_x,tc_nat),V_d,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_mod__eq__0__iff_1) ).
cnf(cls_mult__strict__mono_H_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_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semiring__strict(T_a) ),
file('theBenchmark.p',cls_mult__strict__mono_H_0) ).
cnf(cls_nat__dvd__1__iff__1_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| V_m = c_HOL_Oone__class_Oone(tc_nat) ),
file('theBenchmark.p',cls_nat__dvd__1__iff__1_0) ).
cnf(cls_zero__less__diff_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_zero__less__diff_0) ).
cnf(cls_zero__less__diff_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_zero__less__diff_1) ).
cnf(cls_sum__squares__eq__zero__iff_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
cnf(cls_mult__less__cancel__right__disj_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
cnf(cls_mult__less__cancel__right__disj_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
cnf(cls_mult__less__cancel__left__disj_2,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
cnf(cls_mult__less__cancel__left__disj_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
cnf(cls_vimage__code_0,axiom,
( ~ hBOOL(hAPP(c_Set_Ovimage(V_f,V_A,T_a,T_b),V_x))
| hBOOL(hAPP(V_A,hAPP(V_f,V_x))) ),
file('theBenchmark.p',cls_vimage__code_0) ).
cnf(cls_vimage__code_1,axiom,
( ~ hBOOL(hAPP(V_A,hAPP(V_f,V_x)))
| hBOOL(hAPP(c_Set_Ovimage(V_f,V_A,T_a,T_b),V_x)) ),
file('theBenchmark.p',cls_vimage__code_1) ).
cnf(cls_of__nat__add_0,axiom,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a) = c_HOL_Oplus__class_Oplus(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_Osemiring__1(T_a) ),
file('theBenchmark.p',cls_of__nat__add_0) ).
cnf(cls_diff__less_0,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),V_m,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) ),
file('theBenchmark.p',cls_diff__less_0) ).
cnf(cls_inf1I_0,axiom,
( ~ hBOOL(hAPP(V_A,V_x))
| ~ hBOOL(hAPP(V_B,V_x))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ),
file('theBenchmark.p',cls_inf1I_0) ).
cnf(cls_fun__upd__apply_1,axiom,
( V_z = V_x
| hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_z) = hAPP(V_f,V_z) ),
file('theBenchmark.p',cls_fun__upd__apply_1) ).
cnf(cls_fun__upd__other_0,axiom,
( V_z = V_x
| hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_z) = hAPP(V_f,V_z) ),
file('theBenchmark.p',cls_fun__upd__other_0) ).
cnf(cls_zmod__simps_I1_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_zmod__simps_I1_J_0) ).
cnf(cls_zmod__simps_I2_J_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_zmod__simps_I2_J_0) ).
cnf(cls_add__diff__inverse_0,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = V_m ),
file('theBenchmark.p',cls_add__diff__inverse_0) ).
cnf(cls_inf__period_I4_J_1,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__ring(T_a)
| ~ class_Ring__and__Field_Odvd(T_a) ),
file('theBenchmark.p',cls_inf__period_I4_J_1) ).
cnf(cls_inf__period_I4_J_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__ring(T_a)
| ~ class_Ring__and__Field_Odvd(T_a) ),
file('theBenchmark.p',cls_inf__period_I4_J_0) ).
cnf(cls_add__is__1_1,axiom,
( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_add__is__1_1) ).
cnf(cls_add__is__1_2,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_add__is__1_2) ).
cnf(cls_mult__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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
cnf(cls_zero__le__mult__iff_5,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(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_zero__le__mult__iff_5) ).
cnf(cls_zero__le__mult__iff_4,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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_zero__le__mult__iff_4) ).
cnf(cls_zero__le__square_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__ring__strict(T_a) ),
file('theBenchmark.p',cls_zero__le__square_0) ).
cnf(cls_mult__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(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
cnf(cls_split__mult__pos__le_1,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(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_split__mult__pos__le_1) ).
cnf(cls_split__mult__pos__le_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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ class_Ring__and__Field_Opordered__ring(T_a) ),
file('theBenchmark.p',cls_split__mult__pos__le_0) ).
cnf(cls_mod__mult__mult2_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__mult2_0) ).
cnf(cls_mod__mult__mult1_0,axiom,
( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_c,c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('theBenchmark.p',cls_mod__mult__mult1_0) ).
cnf(cls_dvd__imp__le_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_dvd__imp__le_0) ).
cnf(cls_vimage__empty_0,axiom,
c_Set_Ovimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_vimage__empty_0) ).
cnf(cls_nat__1__eq__mult__iff_0,axiom,
( V_m = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).
cnf(cls_nat__1__eq__mult__iff_1,axiom,
( V_n = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).
cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a) ),
file('theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
cnf(cls_nat__mult__assoc_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat),
file('theBenchmark.p',cls_nat__mult__assoc_0) ).
cnf(cls_class__semiring_Omul__a_0,axiom,
( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Omul__a_0) ).
cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
cnf(cls_comm__semiring__class_Odistrib_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring(T_a) ),
file('theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
cnf(cls_add__mult__distrib_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat),
file('theBenchmark.p',cls_add__mult__distrib_0) ).
cnf(cls_add__mult__distrib2_0,axiom,
c_HOL_Otimes__class_Otimes(V_k,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat),
file('theBenchmark.p',cls_add__mult__distrib2_0) ).
cnf(cls_class__semiring_Omul__d_0,axiom,
( c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('theBenchmark.p',cls_class__semiring_Omul__d_0) ).
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_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_dvd_Ole__less__trans_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) ),
file('theBenchmark.p',cls_dvd_Ole__less__trans_0) ).
cnf(cls_dvd_Oless__le__trans_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat) ),
file('theBenchmark.p',cls_dvd_Oless__le__trans_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_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_Max__mono_0,axiom,
( ~ c_lessequals(V_M,V_N,tc_fun(T_a,tc_bool))
| V_M = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_N,T_a)
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(V_M,T_a),c_Finite__Set_Olinorder__class_OMax(V_N,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_Max__mono_0) ).
cnf(cls_Min__antimono_0,axiom,
( ~ c_lessequals(V_M,V_N,tc_fun(T_a,tc_bool))
| V_M = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_N,T_a)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(V_N,T_a),c_Finite__Set_Olinorder__class_OMin(V_M,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_Min__antimono_0) ).
cnf(cls_subset__insert__iff_0,axiom,
( ~ c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insert__iff_0) ).
cnf(cls_subset__insert__iff_3,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insert__iff_3) ).
cnf(cls_diff__single__insert_0,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_diff__single__insert_0) ).
cnf(cls_card__psubset_0,axiom,
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat)
| c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_card__psubset_0) ).
cnf(cls_card__Diff__subset__Int_0,axiom,
( ~ c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a),tc_nat) ),
file('theBenchmark.p',cls_card__Diff__subset__Int_0) ).
cnf(cls_card__Diff__singleton_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_in(V_x,V_A,T_a)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(V_A,T_a),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
file('theBenchmark.p',cls_card__Diff__singleton_0) ).
cnf(cls_atLeast__iff_0,axiom,
( ~ c_in(V_i,c_SetInterval_Oord__class_OatLeast(V_k,T_a),T_a)
| c_lessequals(V_k,V_i,T_a)
| ~ class_HOL_Oord(T_a) ),
file('theBenchmark.p',cls_atLeast__iff_0) ).
cnf(cls_atLeast__iff_1,axiom,
( ~ c_lessequals(V_k,V_i,T_a)
| c_in(V_i,c_SetInterval_Oord__class_OatLeast(V_k,T_a),T_a)
| ~ class_HOL_Oord(T_a) ),
file('theBenchmark.p',cls_atLeast__iff_1) ).
cnf(cls_le__iff__diff__le__0_1,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__iff__diff__le__0_1) ).
cnf(cls_le__iff__diff__le__0_0,axiom,
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__iff__diff__le__0_0) ).
cnf(cls_insert__Diff__if_1,axiom,
( c_in(V_x,V_B,T_a)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_x,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_insert__Diff__if_1) ).
cnf(cls_Int__insert__left_1,axiom,
( c_in(V_a,V_C,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Int__insert__left_1) ).
cnf(cls_Int__insert__right_1,axiom,
( c_in(V_a,V_A,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Int__insert__right_1) ).
cnf(cls_comm__monoid__add_Ononempty__iff_2,axiom,
( c_in(V_x,V_xa,T_a)
| c_Set_Oinsert(V_x,V_xa,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
cnf(cls_singletonE_0,axiom,
( ~ c_in(V_b,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| V_b = V_a ),
file('theBenchmark.p',cls_singletonE_0) ).
cnf(cls_insert__Diff1_0,axiom,
( ~ c_in(V_x,V_B,T_a)
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_insert__Diff1_0) ).
cnf(cls_psubset__insert__iff_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_psubset__insert__iff_0) ).
cnf(cls_psubset__insert__iff_6,axiom,
( ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_B,T_a)
| c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_psubset__insert__iff_6) ).
cnf(cls_Int__insert__left_0,axiom,
( ~ c_in(V_a,V_C,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_Int__insert__left_0) ).
cnf(cls_Int__insert__right_0,axiom,
( ~ c_in(V_a,V_A,T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_Int__insert__right_0) ).
cnf(cls_singleton__iff_1,axiom,
c_in(V_x,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),
file('theBenchmark.p',cls_singleton__iff_1) ).
cnf(cls_weak__coinduct_0,axiom,
( ~ c_in(V_a,V_X,T_a)
| ~ c_lessequals(V_X,hAPP(V_f,V_X),tc_fun(T_a,tc_bool))
| c_in(V_a,c_Inductive_Ocomplete__lattice__class_Ogfp(V_f,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_weak__coinduct_0) ).
cnf(cls_atLeast__subset__iff_0,axiom,
( ~ c_lessequals(c_SetInterval_Oord__class_OatLeast(V_x,T_a),c_SetInterval_Oord__class_OatLeast(V_y,T_a),tc_fun(T_a,tc_bool))
| c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_atLeast__subset__iff_0) ).
cnf(cls_psubset__eq_2,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| V_A = V_B
| c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_psubset__eq_2) ).
cnf(cls_double__diff_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| c_HOL_Ominus__class_Ominus(V_B,c_HOL_Ominus__class_Ominus(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ),
file('theBenchmark.p',cls_double__diff_0) ).
cnf(cls_Int__mono_0,axiom,
( ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_D,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Int__mono_0) ).
cnf(cls_subset__psubset__trans_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(V_B,V_C,tc_fun(T_a,tc_bool))
| c_HOL_Oord__class_Oless(V_A,V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__psubset__trans_0) ).
cnf(cls_psubset__subset__trans_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| c_HOL_Oord__class_Oless(V_A,V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_psubset__subset__trans_0) ).
cnf(cls_subset__inj__on_0,axiom,
( ~ c_Fun_Oinj__on(V_f,V_B,T_a,T_b)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ),
file('theBenchmark.p',cls_subset__inj__on_0) ).
cnf(cls_subset__UNIV_0,axiom,
c_lessequals(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_subset__UNIV_0) ).
cnf(cls_Int__subset__iff_2,axiom,
( ~ c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_C,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Int__subset__iff_2) ).
cnf(cls_Int__greatest_0,axiom,
( ~ c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_C,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Int__greatest_0) ).
cnf(cls_Int__lower2_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__lower2_0) ).
cnf(cls_Int__lower1_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__lower1_0) ).
cnf(cls_subset__empty_1,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_subset__empty_1) ).
cnf(cls_subset__empty_0,axiom,
( ~ c_lessequals(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__empty_0) ).
cnf(cls_psubset__eq_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_psubset__eq_0) ).
cnf(cls_Diff__mono_0,axiom,
( ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_D,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_C,V_D,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Diff__mono_0) ).
cnf(cls_empty__subsetI_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_empty__subsetI_0) ).
cnf(cls_Int__absorb2_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = V_A ),
file('theBenchmark.p',cls_Int__absorb2_0) ).
cnf(cls_Int__absorb1_0,axiom,
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = V_B ),
file('theBenchmark.p',cls_Int__absorb1_0) ).
cnf(cls_Diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__subset_0) ).
cnf(cls_vimage__mono_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Ovimage(V_f,V_A,T_b,T_a),c_Set_Ovimage(V_f,V_B,T_b,T_a),tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_vimage__mono_0) ).
cnf(cls_Int__subset__iff_1,axiom,
( ~ c_lessequals(V_C,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| c_lessequals(V_C,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Int__subset__iff_1) ).
cnf(cls_Int__subset__iff_0,axiom,
( ~ c_lessequals(V_C,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Int__subset__iff_0) ).
cnf(cls_one__le__mult__iff_2,axiom,
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_one__le__mult__iff_2) ).
cnf(cls_one__le__mult__iff_1,axiom,
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat) ),
file('theBenchmark.p',cls_one__le__mult__iff_1) ).
cnf(cls_one__le__mult__iff_0,axiom,
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat) ),
file('theBenchmark.p',cls_one__le__mult__iff_0) ).
cnf(cls_inj__on__image__set__diff_0,axiom,
( ~ c_Fun_Oinj__on(V_f,V_C,T_a,T_b)
| ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(V_f,V_A,T_a,T_b),c_Set_Oimage(V_f,V_B,T_a,T_b),tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_inj__on__image__set__diff_0) ).
cnf(cls_inj__on__inv__into_0,axiom,
( ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_b,T_a),V_B,T_a,T_b) ),
file('theBenchmark.p',cls_inj__on__inv__into_0) ).
cnf(cls_inj__image__subset__iff_1,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oimage(V_f,V_A,T_a,T_b),c_Set_Oimage(V_f,V_B,T_a,T_b),tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_inj__image__subset__iff_1) ).
cnf(cls_inj__image__subset__iff_0,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| ~ c_lessequals(c_Set_Oimage(V_f,V_A,T_a,T_b),c_Set_Oimage(V_f,V_B,T_a,T_b),tc_fun(T_b,tc_bool))
| c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_inj__image__subset__iff_0) ).
cnf(cls_inj__on__image__Int_0,axiom,
( ~ c_Fun_Oinj__on(V_f,V_C,T_a,T_b)
| ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| c_Set_Oimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(V_f,V_A,T_a,T_b),c_Set_Oimage(V_f,V_B,T_a,T_b),tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_inj__on__image__Int_0) ).
cnf(cls_inv__into__image__cancel_0,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_lessequals(V_S,V_A,tc_fun(T_a,tc_bool))
| c_Set_Oimage(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),c_Set_Oimage(V_f,V_S,T_a,T_b),T_b,T_a) = V_S ),
file('theBenchmark.p',cls_inv__into__image__cancel_0) ).
cnf(cls_card__eq__0__iff_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ocard(V_A,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_card__eq__0__iff_0) ).
cnf(cls_psubset__card__mono_0,axiom,
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ),
file('theBenchmark.p',cls_psubset__card__mono_0) ).
cnf(cls_card__gt__0__iff_1,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(V_A,T_a),tc_nat)
| c_Finite__Set_Ofinite(V_A,T_a) ),
file('theBenchmark.p',cls_card__gt__0__iff_1) ).
cnf(cls_le__neq__implies__less_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| V_m = V_n
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_le__neq__implies__less_0) ).
cnf(cls_le__eq__less__or__eq_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| V_m = V_n ),
file('theBenchmark.p',cls_le__eq__less__or__eq_0) ).
cnf(cls_nat__less__le_2,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| V_m = V_n
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__less__le_2) ).
cnf(cls_mult__le__cancel2_2,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__le__cancel2_2) ).
cnf(cls_mult__le__cancel1_2,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__le__cancel1_2) ).
cnf(cls_mult__le__mono2_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__le__mono2_0) ).
cnf(cls_mult__le__mono1_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__le__mono1_0) ).
cnf(cls_le__0__eq_1,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_le__0__eq_1) ).
cnf(cls_inc__induct_2,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ hBOOL(hAPP(V_P,V_j))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(V_P,V_j)))
| hBOOL(hAPP(V_P,V_i)) ),
file('theBenchmark.p',cls_inc__induct_2) ).
cnf(cls_nat__add__left__cancel__le_1,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
cnf(cls_nat__add__left__cancel__le_0,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
cnf(cls_add__le__mono1_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_add__le__mono1_0) ).
cnf(cls_nat__less__le_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__less__le_0) ).
cnf(cls_termination__basic__simps_I5_J_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
| c_lessequals(V_x,V_y,tc_nat) ),
file('theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
cnf(cls_le__iff__add_1,axiom,
c_lessequals(V_m,c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat),tc_nat),
file('theBenchmark.p',cls_le__iff__add_1) ).
cnf(cls_le__add2_0,axiom,
c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat),
file('theBenchmark.p',cls_le__add2_0) ).
cnf(cls_le__add1_0,axiom,
c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat),
file('theBenchmark.p',cls_le__add1_0) ).
cnf(cls_le__0__eq_0,axiom,
( ~ c_lessequals(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_le__0__eq_0) ).
cnf(cls_add__le__mono_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ c_lessequals(V_k,V_l,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_add__le__mono_0) ).
cnf(cls_trans__le__add2_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_trans__le__add2_0) ).
cnf(cls_trans__le__add1_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_trans__le__add1_0) ).
cnf(cls_add__leE_1,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_add__leE_1) ).
cnf(cls_add__leE_0,axiom,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_add__leE_0) ).
cnf(cls_termination__basic__simps_I4_J_0,axiom,
( ~ c_lessequals(V_x,V_z,tc_nat)
| c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
cnf(cls_termination__basic__simps_I3_J_0,axiom,
( ~ c_lessequals(V_x,V_y,tc_nat)
| c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
cnf(cls_le0_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),
file('theBenchmark.p',cls_le0_0) ).
cnf(cls_mod__less__eq__dividend_0,axiom,
c_lessequals(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_m,tc_nat),
file('theBenchmark.p',cls_mod__less__eq__dividend_0) ).
cnf(cls_le__square_0,axiom,
c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat),
file('theBenchmark.p',cls_le__square_0) ).
cnf(cls_mult__le__mono_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ c_lessequals(V_k,V_l,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_l,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_mult__le__mono_0) ).
cnf(cls_le__cube_0,axiom,
c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat),tc_nat),
file('theBenchmark.p',cls_le__cube_0) ).
cnf(cls_diff__Suc__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_diff__Suc__less_0) ).
cnf(cls_Suc__pred_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = V_n ),
file('theBenchmark.p',cls_Suc__pred_0) ).
cnf(cls_image__cong_1,axiom,
( c_Set_Oimage(V_f,V_x,T_a,T_b) = c_Set_Oimage(V_g,V_x,T_a,T_b)
| hAPP(V_f,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(V_x,V_f,V_g,T_a,T_b)) != hAPP(V_g,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(V_x,V_f,V_g,T_a,T_b)) ),
file('theBenchmark.p',cls_image__cong_1) ).
cnf(cls_image__is__empty_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| c_Set_Oimage(V_f,V_A,T_b,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_image__is__empty_0) ).
cnf(cls_empty__is__image_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oimage(V_f,V_A,T_b,T_a) ),
file('theBenchmark.p',cls_empty__is__image_0) ).
cnf(cls_image__empty_0,axiom,
c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_image__empty_0) ).
cnf(cls_empty__is__image_1,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a),
file('theBenchmark.p',cls_empty__is__image_1) ).
cnf(cls_nat__le__add__iff2_1,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ c_lessequals(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__le__add__iff2_1) ).
cnf(cls_nat__le__add__iff2_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
| c_lessequals(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__le__add__iff2_0) ).
cnf(cls_nat__le__add__iff1_1,axiom,
( ~ c_lessequals(V_j,V_i,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__le__add__iff1_1) ).
cnf(cls_nat__le__add__iff1_0,axiom,
( ~ c_lessequals(V_j,V_i,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__le__add__iff1_0) ).
cnf(cls_nat__eq__add__iff2_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ),
file('theBenchmark.p',cls_nat__eq__add__iff2_1) ).
cnf(cls_nat__eq__add__iff2_0,axiom,
( V_m = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__eq__add__iff2_0) ).
cnf(cls_nat__eq__add__iff1_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat) = V_n
| ~ c_lessequals(V_j,V_i,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__eq__add__iff1_0) ).
cnf(cls_nat__eq__add__iff1_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),tc_nat)
| ~ c_lessequals(V_j,V_i,tc_nat) ),
file('theBenchmark.p',cls_nat__eq__add__iff1_1) ).
cnf(cls_nat__diff__add__eq2_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_u,tc_nat),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_nat__diff__add__eq2_0) ).
cnf(cls_nat__diff__add__eq1_0,axiom,
( ~ c_lessequals(V_j,V_i,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),V_m,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_u,tc_nat),V_m,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_nat__diff__add__eq1_0) ).
cnf(cls_diffs0__imp__equal_0,axiom,
( V_m = V_n
| c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_diffs0__imp__equal_0) ).
cnf(cls_less__imp__diff__less_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ),
file('theBenchmark.p',cls_less__imp__diff__less_0) ).
cnf(cls_dvd__diff__nat_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_dvd__diff__nat_0) ).
cnf(cls_minus__nat_Odiff__0_0,axiom,
c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m,
file('theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
cnf(cls_diff__self__eq__0_0,axiom,
c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_diff__self__eq__0_0) ).
cnf(cls_diff__less__mono2_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_l,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_diff__less__mono2_0) ).
cnf(cls_nat__diff__split__asm_1,axiom,
( hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_b,V_x,tc_nat),V_b,tc_nat))) ),
file('theBenchmark.p',cls_nat__diff__split__asm_1) ).
cnf(cls_nat__diff__split_1,axiom,
( hBOOL(hAPP(V_P,V_d))
| ~ hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_b,V_d,tc_nat),V_b,tc_nat))) ),
file('theBenchmark.p',cls_nat__diff__split_1) ).
cnf(cls_zero__induct__lemma_1,axiom,
( ~ hBOOL(hAPP(V_P,V_k))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(V_P)))
| hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(V_k,V_i,tc_nat))) ),
file('theBenchmark.p',cls_zero__induct__lemma_1) ).
cnf(cls_diff__diff__left_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat),
file('theBenchmark.p',cls_diff__diff__left_0) ).
cnf(cls_diff__0__eq__0_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_diff__0__eq__0_0) ).
cnf(cls_diff__cancel2_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),
file('theBenchmark.p',cls_diff__cancel2_0) ).
cnf(cls_diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),
file('theBenchmark.p',cls_diff__cancel_0) ).
cnf(cls_diff__mult__distrib2_0,axiom,
c_HOL_Otimes__class_Otimes(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat),
file('theBenchmark.p',cls_diff__mult__distrib2_0) ).
cnf(cls_diff__mult__distrib_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat),
file('theBenchmark.p',cls_diff__mult__distrib_0) ).
cnf(cls_diff__add__inverse2_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m,
file('theBenchmark.p',cls_diff__add__inverse2_0) ).
cnf(cls_diff__add__inverse_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_n,tc_nat) = V_m,
file('theBenchmark.p',cls_diff__add__inverse_0) ).
cnf(cls_card__Diff1__less_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_in(V_x,V_A,T_a)
| c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ),
file('theBenchmark.p',cls_card__Diff1__less_0) ).
cnf(cls_card__Diff2__less_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_in(V_x,V_A,T_a)
| ~ c_in(V_y,V_A,T_a)
| c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_y,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ),
file('theBenchmark.p',cls_card__Diff2__less_0) ).
cnf(cls_atLeast__subset__iff_1,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(c_SetInterval_Oord__class_OatLeast(V_x,T_a),c_SetInterval_Oord__class_OatLeast(V_y,T_a),tc_fun(T_a,tc_bool))
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_atLeast__subset__iff_1) ).
cnf(cls_rangeI_0,axiom,
c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a),T_a),
file('theBenchmark.p',cls_rangeI_0) ).
cnf(cls_inv__into__into_0,axiom,
( ~ c_in(V_x,c_Set_Oimage(V_f,V_A,T_b,T_a),T_a)
| c_in(hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_b,T_a),V_x),V_A,T_b) ),
file('theBenchmark.p',cls_inv__into__into_0) ).
cnf(cls_inv__into__injective_0,axiom,
( ~ c_in(V_x,c_Set_Oimage(V_f,V_A,T_a,T_b),T_b)
| ~ c_in(V_y,c_Set_Oimage(V_f,V_A,T_a,T_b),T_b)
| V_x = V_y
| hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),V_x) != hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),V_y) ),
file('theBenchmark.p',cls_inv__into__injective_0) ).
cnf(cls_imageE_1,axiom,
( ~ c_in(V_b,c_Set_Oimage(V_f,V_A,T_b,T_a),T_a)
| c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(V_A,V_b,V_f,T_b,T_a),V_A,T_b) ),
file('theBenchmark.p',cls_imageE_1) ).
cnf(cls_image__iff_1,axiom,
( ~ c_in(V_z,c_Set_Oimage(V_f,V_A,T_b,T_a),T_a)
| V_z = hAPP(V_f,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(V_A,V_f,V_z,T_b,T_a)) ),
file('theBenchmark.p',cls_image__iff_1) ).
cnf(cls_image__cong_0,axiom,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(V_x,V_f,V_g,T_a,T_b),V_x,T_a)
| c_Set_Oimage(V_f,V_x,T_a,T_b) = c_Set_Oimage(V_g,V_x,T_a,T_b) ),
file('theBenchmark.p',cls_image__cong_0) ).
cnf(cls_f__inv__into__f_0,axiom,
( ~ c_in(V_y,c_Set_Oimage(V_f,V_A,T_b,T_a),T_a)
| hAPP(V_f,hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_b,T_a),V_y)) = V_y ),
file('theBenchmark.p',cls_f__inv__into__f_0) ).
cnf(cls_image__iff_0,axiom,
( ~ c_in(V_z,c_Set_Oimage(V_f,V_A,T_b,T_a),T_a)
| c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(V_A,V_f,V_z,T_b,T_a),V_A,T_b) ),
file('theBenchmark.p',cls_image__iff_0) ).
cnf(cls_fun__upd__image_1,axiom,
( c_in(V_x,V_A,T_b)
| c_Set_Oimage(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_A,T_b,T_a) = c_Set_Oimage(V_f,V_A,T_b,T_a) ),
file('theBenchmark.p',cls_fun__upd__image_1) ).
cnf(cls_imageE_0,axiom,
( ~ c_in(V_b,c_Set_Oimage(V_f,V_A,T_b,T_a),T_a)
| V_b = hAPP(V_f,c_ATP__Linkup_Osko__Set__XimageE__1__1(V_A,V_b,V_f,T_b,T_a)) ),
file('theBenchmark.p',cls_imageE_0) ).
cnf(cls_of__nat__le__iff_1,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(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__le__iff_1) ).
cnf(cls_of__nat__le__iff_0,axiom,
( ~ c_lessequals(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_lessequals(V_m,V_n,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('theBenchmark.p',cls_of__nat__le__iff_0) ).
cnf(cls_finite__Diff__insert_0,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),T_a)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_finite__Diff__insert_0) ).
cnf(cls_finite__Diff__insert_1,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_finite__Diff__insert_1) ).
cnf(cls_card__Diff__singleton__if_1,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = c_Finite__Set_Ocard(V_A,T_a) ),
file('theBenchmark.p',cls_card__Diff__singleton__if_1) ).
cnf(cls_finite__imageD_0,axiom,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(V_f,V_A,T_b,T_a),T_a)
| ~ c_Fun_Oinj__on(V_f,V_A,T_b,T_a)
| c_Finite__Set_Ofinite(V_A,T_b) ),
file('theBenchmark.p',cls_finite__imageD_0) ).
cnf(cls_subset__singletonD_0,axiom,
( ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_subset__singletonD_0) ).
cnf(cls_full__nat__induct_0,axiom,
( ~ c_lessequals(c_Suc(V_m),c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(V_P),tc_nat)
| hBOOL(hAPP(V_P,V_m))
| hBOOL(hAPP(V_P,V_n)) ),
file('theBenchmark.p',cls_full__nat__induct_0) ).
cnf(cls_Suc__mult__le__cancel1_0,axiom,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).
cnf(cls_Suc__mult__le__cancel1_1,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_Suc__mult__le__cancel1_1) ).
cnf(cls_le__less__Suc__eq_1,axiom,
( c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat)
| ~ c_lessequals(V_x,V_x,tc_nat) ),
file('theBenchmark.p',cls_le__less__Suc__eq_1) ).
cnf(cls_less__Suc__eq__le_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_less__Suc__eq__le_0) ).
cnf(cls_less__Suc__eq__le_1,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ),
file('theBenchmark.p',cls_less__Suc__eq__le_1) ).
cnf(cls_Suc__leI_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_lessequals(c_Suc(V_m),V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__leI_0) ).
cnf(cls_Suc__le__eq_0,axiom,
( ~ c_lessequals(c_Suc(V_m),V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__le__eq_0) ).
cnf(cls_less__eq__Suc__le_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| c_lessequals(c_Suc(V_n),V_m,tc_nat) ),
file('theBenchmark.p',cls_less__eq__Suc__le_0) ).
cnf(cls_less__eq__Suc__le_1,axiom,
( ~ c_lessequals(c_Suc(V_n),V_m,tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ),
file('theBenchmark.p',cls_less__eq__Suc__le_1) ).
cnf(cls_inc__induct_1,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ hBOOL(hAPP(V_P,V_j))
| hBOOL(hAPP(V_P,c_Suc(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(V_P,V_j))))
| hBOOL(hAPP(V_P,V_i)) ),
file('theBenchmark.p',cls_inc__induct_1) ).
cnf(cls_Suc__le__D_0,axiom,
( ~ c_lessequals(c_Suc(V_n),V_m_H,tc_nat)
| V_m_H = c_Suc(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(V_m_H)) ),
file('theBenchmark.p',cls_Suc__le__D_0) ).
cnf(cls_Suc__le__D__lemma_0,axiom,
( ~ c_lessequals(c_Suc(V_n),V_m_H,tc_nat)
| c_lessequals(V_n,c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(V_P,V_n),tc_nat)
| hBOOL(hAPP(V_P,V_m_H)) ),
file('theBenchmark.p',cls_Suc__le__D__lemma_0) ).
cnf(cls_Suc__le__D__lemma_1,axiom,
( ~ c_lessequals(c_Suc(V_n),V_m_H,tc_nat)
| ~ hBOOL(hAPP(V_P,c_Suc(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(V_P,V_n))))
| hBOOL(hAPP(V_P,V_m_H)) ),
file('theBenchmark.p',cls_Suc__le__D__lemma_1) ).
cnf(cls_le__less__Suc__eq_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| V_n = V_m ),
file('theBenchmark.p',cls_le__less__Suc__eq_0) ).
cnf(cls_card__insert_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a)) ),
file('theBenchmark.p',cls_card__insert_0) ).
cnf(cls_card__Diff1__le_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ),
file('theBenchmark.p',cls_card__Diff1__le_0) ).
cnf(cls_subset__image__iff_1,axiom,
( ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ),
file('theBenchmark.p',cls_subset__image__iff_1) ).
cnf(cls_image__diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_image__diff__subset_0) ).
cnf(cls_subset__image__iff_0,axiom,
( ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| c_lessequals(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(V_A,V_B,V_f,T_b,T_a),V_A,tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_subset__image__iff_0) ).
cnf(cls_image__vimage__subset_0,axiom,
c_lessequals(c_Set_Oimage(V_f,c_Set_Ovimage(V_f,V_A,T_b,T_a),T_b,T_a),V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_image__vimage__subset_0) ).
cnf(cls_image__Int__subset_0,axiom,
c_lessequals(c_Set_Oimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_image__Int__subset_0) ).
cnf(cls_card__eq__UNIV__imp__eq__UNIV_0,axiom,
( V_A = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)
| c_Finite__Set_Ocard(V_A,T_a) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).
cnf(cls_card__eq__0__iff_2,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ocard(V_A,T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_card__eq__0__iff_2) ).
cnf(cls_diff__Suc__eq__diff__pred_0,axiom,
c_HOL_Ominus__class_Ominus(V_m,c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_n,tc_nat),
file('theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).
cnf(cls_zero__induct__lemma_0,axiom,
( ~ hBOOL(hAPP(V_P,V_k))
| hBOOL(hAPP(V_P,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(V_P))))
| hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(V_k,V_i,tc_nat))) ),
file('theBenchmark.p',cls_zero__induct__lemma_0) ).
cnf(cls_diff__less__Suc_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat),
file('theBenchmark.p',cls_diff__less__Suc_0) ).
cnf(cls_diff__Suc__1_0,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(V_n),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = V_n,
file('theBenchmark.p',cls_diff__Suc__1_0) ).
cnf(cls_card__eq__SucD_2,axiom,
( c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(V_A,V_k,T_a),T_a) = V_k
| c_Finite__Set_Ocard(V_A,T_a) != c_Suc(V_k) ),
file('theBenchmark.p',cls_card__eq__SucD_2) ).
cnf(cls_card__Suc__eq_2,axiom,
( c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(V_A,V_k,T_a),T_a) = V_k
| c_Finite__Set_Ocard(V_A,T_a) != c_Suc(V_k) ),
file('theBenchmark.p',cls_card__Suc__eq_2) ).
cnf(cls_le__add__diff_0,axiom,
( ~ c_lessequals(V_k,V_n,tc_nat)
| c_lessequals(V_m,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_le__add__diff_0) ).
cnf(cls_diff__less__mono_0,axiom,
( ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_nat)
| ~ c_lessequals(V_c,V_a,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_c,tc_nat),c_HOL_Ominus__class_Ominus(V_b,V_c,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_diff__less__mono_0) ).
cnf(cls_diff__is__0__eq_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_diff__is__0__eq_0) ).
cnf(cls_diff__is__0__eq_1,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_diff__is__0__eq_1) ).
cnf(cls_dvd__diffD_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)
| ~ c_lessequals(V_n,V_m,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,tc_nat) ),
file('theBenchmark.p',cls_dvd__diffD_0) ).
cnf(cls_dvd__diffD1_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,tc_nat)
| ~ c_lessequals(V_n,V_m,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat) ),
file('theBenchmark.p',cls_dvd__diffD1_0) ).
cnf(cls_le__diff__conv2_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| ~ c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) ),
file('theBenchmark.p',cls_le__diff__conv2_0) ).
cnf(cls_le__diff__conv2_1,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)
| c_lessequals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_le__diff__conv2_1) ).
cnf(cls_le__mod__geq_0,axiom,
( ~ c_lessequals(V_n,V_m,tc_nat)
| c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat) ),
file('theBenchmark.p',cls_le__mod__geq_0) ).
cnf(cls_le__diff__conv_0,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat)
| c_lessequals(V_j,c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_le__diff__conv_0) ).
cnf(cls_le__diff__conv_1,axiom,
( ~ c_lessequals(V_j,c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) ),
file('theBenchmark.p',cls_le__diff__conv_1) ).
cnf(cls_diff__add__assoc_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_diff__add__assoc_0) ).
cnf(cls_diff__add__assoc2_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) ),
file('theBenchmark.p',cls_diff__add__assoc2_0) ).
cnf(cls_diff__diff__right_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_HOL_Ominus__class_Ominus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) ),
file('theBenchmark.p',cls_diff__diff__right_0) ).
cnf(cls_le__imp__diff__is__add_1,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_i,tc_nat),V_i,tc_nat) = V_k
| ~ c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_k,V_i,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_le__imp__diff__is__add_1) ).
cnf(cls_le__imp__diff__is__add_0,axiom,
( V_j = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat),V_i,tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ),
file('theBenchmark.p',cls_le__imp__diff__is__add_0) ).
cnf(cls_le__add__diff__inverse_0,axiom,
( ~ c_lessequals(V_n,V_m,tc_nat)
| c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = V_m ),
file('theBenchmark.p',cls_le__add__diff__inverse_0) ).
cnf(cls_le__add__diff__inverse2_0,axiom,
( ~ c_lessequals(V_n,V_m,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m ),
file('theBenchmark.p',cls_le__add__diff__inverse2_0) ).
cnf(cls_add__diff__assoc_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_HOL_Oplus__class_Oplus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) ),
file('theBenchmark.p',cls_add__diff__assoc_0) ).
cnf(cls_add__diff__assoc2_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_k,tc_nat) ),
file('theBenchmark.p',cls_add__diff__assoc2_0) ).
cnf(cls_less__diff__iff_0,axiom,
( ~ c_lessequals(V_k,V_m,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_less__diff__iff_0) ).
cnf(cls_less__diff__iff_1,axiom,
( ~ c_lessequals(V_k,V_m,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_less__diff__iff_1) ).
cnf(cls_card__image_0,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| c_Finite__Set_Ocard(c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Finite__Set_Ocard(V_A,T_a) ),
file('theBenchmark.p',cls_card__image_0) ).
cnf(cls_card__Suc__Diff1_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_in(V_x,V_A,T_a)
| c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a)) = c_Finite__Set_Ocard(V_A,T_a) ),
file('theBenchmark.p',cls_card__Suc__Diff1_0) ).
cnf(cls_card__Diff__insert_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_in(V_a,V_A,T_a)
| c_in(V_a,V_B,T_a)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),T_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
file('theBenchmark.p',cls_card__Diff__insert_0) ).
cnf(cls_Min__le_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_in(V_x,V_A,T_a)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(V_A,T_a),V_x,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_Min__le_0) ).
cnf(cls_Max__ge_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_in(V_x,V_A,T_a)
| c_lessequals(V_x,c_Finite__Set_Olinorder__class_OMax(V_A,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('theBenchmark.p',cls_Max__ge_0) ).
cnf(cls_psubset__insert__iff_2,axiom,
( ~ c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a)
| c_in(V_x,V_A,T_a)
| c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_psubset__insert__iff_2) ).
cnf(cls_psubset__insert__iff_3,axiom,
( c_in(V_x,V_B,T_a)
| c_in(V_x,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_psubset__insert__iff_3) ).
cnf(cls_psubset__insert__iff_7,axiom,
( ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_psubset__insert__iff_7) ).
cnf(cls_lift__Suc__mono__le_0,axiom,
( ~ c_lessequals(hAPP(V_f,c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(V_f,T_a)),hAPP(V_f,c_Suc(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(V_f,T_a))),T_a)
| ~ c_lessequals(V_n,V_n_H,tc_nat)
| c_lessequals(hAPP(V_f,V_n),hAPP(V_f,V_n_H),T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_lift__Suc__mono__le_0) ).
cnf(cls_image__subsetI_0,axiom,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(V_A,V_B,V_f,T_a,T_b),V_A,T_a)
| c_lessequals(c_Set_Oimage(V_f,V_A,T_a,T_b),V_B,tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_image__subsetI_0) ).
cnf(cls_image__subset__iff_2,axiom,
( ~ c_in(hAPP(V_f,c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(V_A,V_B,V_f,T_b,T_a)),V_B,T_a)
| c_lessequals(c_Set_Oimage(V_f,V_A,T_b,T_a),V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_image__subset__iff_2) ).
cnf(cls_image__subset__iff_1,axiom,
( c_in(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(V_A,V_B,V_f,T_b,T_a),V_A,T_b)
| c_lessequals(c_Set_Oimage(V_f,V_A,T_b,T_a),V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_image__subset__iff_1) ).
cnf(cls_weak__coinduct__image_0,axiom,
( ~ c_in(V_a,V_X,T_a)
| ~ c_lessequals(c_Set_Oimage(V_g,V_X,T_a,T_b),hAPP(V_f,c_Set_Oimage(V_g,V_X,T_a,T_b)),tc_fun(T_b,tc_bool))
| c_in(hAPP(V_g,V_a),c_Inductive_Ocomplete__lattice__class_Ogfp(V_f,tc_fun(T_b,tc_bool)),T_b) ),
file('theBenchmark.p',cls_weak__coinduct__image_0) ).
cnf(cls_image__subsetI_1,axiom,
( ~ c_in(hAPP(V_f,c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(V_A,V_B,V_f,T_a,T_b)),V_B,T_b)
| c_lessequals(c_Set_Oimage(V_f,V_A,T_a,T_b),V_B,tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_image__subsetI_1) ).
cnf(cls_finite__surj__inj_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_lessequals(V_A,c_Set_Oimage(V_f,V_A,T_a,T_a),tc_fun(T_a,tc_bool))
| c_Fun_Oinj__on(V_f,V_A,T_a,T_a) ),
file('theBenchmark.p',cls_finite__surj__inj_0) ).
cnf(cls_finite__subset__image_2,axiom,
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| V_B = c_Set_Oimage(V_f,c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b,T_a) ),
file('theBenchmark.p',cls_finite__subset__image_2) ).
cnf(cls_finite__subset__image_1,axiom,
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),T_b) ),
file('theBenchmark.p',cls_finite__subset__image_1) ).
cnf(cls_endo__inj__surj_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_lessequals(c_Set_Oimage(V_f,V_A,T_a,T_a),V_A,tc_fun(T_a,tc_bool))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
| c_Set_Oimage(V_f,V_A,T_a,T_a) = V_A ),
file('theBenchmark.p',cls_endo__inj__surj_0) ).
cnf(cls_finite__subset__image_0,axiom,
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| c_lessequals(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(V_A,V_B,V_f,T_b,T_a),V_A,tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_finite__subset__image_0) ).
cnf(cls_of__nat__diff_0,axiom,
( ~ c_lessequals(V_n,V_m,tc_nat)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Ominus__class_Ominus(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_Oring__1(T_a) ),
file('theBenchmark.p',cls_of__nat__diff_0) ).
cnf(cls_eq__card__imp__inj__on_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ocard(c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) != c_Finite__Set_Ocard(V_A,T_a) ),
file('theBenchmark.p',cls_eq__card__imp__inj__on_0) ).
cnf(cls_inj__on__iff__eq__card_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| c_Finite__Set_Ocard(c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Finite__Set_Ocard(V_A,T_a) ),
file('theBenchmark.p',cls_inj__on__iff__eq__card_0) ).
cnf(cls_diff__Suc__diff__eq2_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),V_m,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(V_j),c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
cnf(cls_diff__Suc__diff__eq1_0,axiom,
( ~ c_lessequals(V_k,V_j,tc_nat)
| c_HOL_Ominus__class_Ominus(V_m,c_Suc(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_Suc(V_j),tc_nat) ),
file('theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).
cnf(cls_card__Suc__eq_5,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))
| c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_card__Suc__eq_5) ).
cnf(cls_card__Suc__eq_4,axiom,
( c_Finite__Set_Ocard(V_xa,T_a) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_xa,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_xa,T_a))
| c_in(V_x,V_xa,T_a) ),
file('theBenchmark.p',cls_card__Suc__eq_4) ).
cnf(cls_card__bij__eq_0,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_lessequals(c_Set_Oimage(V_f,V_A,T_a,T_b),V_B,tc_fun(T_b,tc_bool))
| ~ c_Fun_Oinj__on(V_g,V_B,T_b,T_a)
| ~ c_lessequals(c_Set_Oimage(V_g,V_B,T_b,T_a),V_A,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_B,T_b)
| c_Finite__Set_Ocard(V_A,T_a) = c_Finite__Set_Ocard(V_B,T_b) ),
file('theBenchmark.p',cls_card__bij__eq_0) ).
cnf(cls_card__Diff__subset_0,axiom,
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ),
file('theBenchmark.p',cls_card__Diff__subset_0) ).
cnf(cls_card__inj__on__le_0,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_lessequals(c_Set_Oimage(V_f,V_A,T_a,T_b),V_B,tc_fun(T_b,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_b)
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_b),tc_nat) ),
file('theBenchmark.p',cls_card__inj__on__le_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_nat__le__linear_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(V_n,V_m,tc_nat) ),
file('theBenchmark.p',cls_nat__le__linear_0) ).
cnf(cls_Suc__le__mono_1,axiom,
( ~ c_lessequals(V_n,V_m,tc_nat)
| c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ),
file('theBenchmark.p',cls_Suc__le__mono_1) ).
cnf(cls_Suc__le__mono_0,axiom,
( ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat)
| c_lessequals(V_n,V_m,tc_nat) ),
file('theBenchmark.p',cls_Suc__le__mono_0) ).
cnf(cls_insert__mono_0,axiom,
( ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_insert__mono_0) ).
cnf(cls_subset__image__iff_2,axiom,
( c_lessequals(c_Set_Oimage(V_f,V_x,T_b,T_a),c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_x,V_A,tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_subset__image__iff_2) ).
cnf(cls_image__mono_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oimage(V_f,V_A,T_a,T_b),c_Set_Oimage(V_f,V_B,T_a,T_b),tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_image__mono_0) ).
cnf(cls_le__eqI_1,axiom,
( ~ c_lessequals(V_y_H,V_x_H,T_a)
| c_lessequals(V_y,V_x,T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__eqI_1) ).
cnf(cls_le__eqI_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_y_H,V_x_H,T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('theBenchmark.p',cls_le__eqI_0) ).
cnf(cls_insert__iff_2,axiom,
( ~ c_in(V_a,V_A,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a) ),
file('theBenchmark.p',cls_insert__iff_2) ).
cnf(cls_insertCI_0,axiom,
( ~ c_in(V_a,V_B,T_a)
| c_in(V_a,c_Set_Oinsert(V_b,V_B,T_a),T_a) ),
file('theBenchmark.p',cls_insertCI_0) ).
cnf(cls_rev__finite__subset_0,axiom,
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_Finite__Set_Ofinite(V_A,T_a) ),
file('theBenchmark.p',cls_rev__finite__subset_0) ).
cnf(cls_rev__predicate1D_0,axiom,
( ~ hBOOL(hAPP(V_P,V_x))
| ~ c_lessequals(V_P,V_Q,tc_fun(T_a,tc_bool))
| hBOOL(hAPP(V_Q,V_x)) ),
file('theBenchmark.p',cls_rev__predicate1D_0) ).
cnf(cls_finite__subset_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ),
file('theBenchmark.p',cls_finite__subset_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_predicate1D_0,axiom,
( ~ c_lessequals(V_P,V_Q,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(V_P,V_x))
| hBOOL(hAPP(V_Q,V_x)) ),
file('theBenchmark.p',cls_predicate1D_0) ).
cnf(cls_subset__trans_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__trans_0) ).
cnf(cls_subset__refl_0,axiom,
c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_subset__refl_0) ).
cnf(cls_subset__iff_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_t,V_A,T_a)
| c_in(V_t,V_B,T_a) ),
file('theBenchmark.p',cls_subset__iff_0) ).
cnf(cls_set__rev__mp_0,axiom,
( ~ c_in(V_x,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ),
file('theBenchmark.p',cls_set__rev__mp_0) ).
cnf(cls_equalityE_0,axiom,
c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_equalityE_0) ).
cnf(cls_eq__imp__le_0,axiom,
c_lessequals(V_x,V_x,tc_nat),
file('theBenchmark.p',cls_eq__imp__le_0) ).
cnf(cls_le__trans_0,axiom,
( ~ c_lessequals(V_i,V_j,tc_nat)
| ~ c_lessequals(V_j,V_k,tc_nat)
| c_lessequals(V_i,V_k,tc_nat) ),
file('theBenchmark.p',cls_le__trans_0) ).
cnf(cls_subsetD_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a) ),
file('theBenchmark.p',cls_subsetD_0) ).
cnf(cls_le__refl_0,axiom,
c_lessequals(V_n,V_n,tc_nat),
file('theBenchmark.p',cls_le__refl_0) ).
cnf(cls_set__mp_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_a)
| c_in(V_x,V_B,T_a) ),
file('theBenchmark.p',cls_set__mp_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_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_n__not__Suc__n_0,axiom,
V_n != c_Suc(V_n),
file('theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(V_n) != V_n,
file('theBenchmark.p',cls_Suc__n__not__n_0) ).
cnf(cls_insert__subset_2,axiom,
( ~ c_in(V_x,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_insert__subset_2) ).
cnf(cls_Suc__n__not__le__n_0,axiom,
~ c_lessequals(c_Suc(V_n),V_n,tc_nat),
file('theBenchmark.p',cls_Suc__n__not__le__n_0) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)),
file('theBenchmark.p',cls_insert__code_1) ).
cnf(cls_le__SucI_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(V_m,c_Suc(V_n),tc_nat) ),
file('theBenchmark.p',cls_le__SucI_0) ).
cnf(cls_Suc__leD_0,axiom,
( ~ c_lessequals(c_Suc(V_m),V_n,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_Suc__leD_0) ).
cnf(cls_image__insert_0,axiom,
c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a),
file('theBenchmark.p',cls_image__insert_0) ).
cnf(cls_card__insert__if_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_in(V_x,V_A,T_a)
| c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Finite__Set_Ocard(V_A,T_a) ),
file('theBenchmark.p',cls_card__insert__if_0) ).
cnf(cls_finite__imageI_0,axiom,
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
file('theBenchmark.p',cls_finite__imageI_0) ).
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_set__eq__subset_2,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| V_A = V_B ),
file('theBenchmark.p',cls_set__eq__subset_2) ).
cnf(cls_le__antisym_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(V_n,V_m,tc_nat)
| V_m = V_n ),
file('theBenchmark.p',cls_le__antisym_0) ).
cnf(cls_equalityI_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| V_A = V_B ),
file('theBenchmark.p',cls_equalityI_0) ).
cnf(cls_insertE_0,axiom,
( ~ c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a)
| V_a = V_b
| c_in(V_a,V_A,T_a) ),
file('theBenchmark.p',cls_insertE_0) ).
cnf(cls_card__seteq_0,axiom,
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(V_B,T_a),c_Finite__Set_Ocard(V_A,T_a),tc_nat)
| V_A = V_B ),
file('theBenchmark.p',cls_card__seteq_0) ).
cnf(cls_diff__Suc__Suc_0,axiom,
c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),
file('theBenchmark.p',cls_diff__Suc__Suc_0) ).
cnf(cls_nat_Oinject_0,axiom,
( V_nat = V_nat_H
| c_Suc(V_nat) != c_Suc(V_nat_H) ),
file('theBenchmark.p',cls_nat_Oinject_0) ).
cnf(cls_Suc__inject_0,axiom,
( V_x = V_y
| c_Suc(V_x) != c_Suc(V_y) ),
file('theBenchmark.p',cls_Suc__inject_0) ).
cnf(cls_card__insert__le_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a),tc_nat) ),
file('theBenchmark.p',cls_card__insert__le_0) ).
cnf(cls_finite__insert_1,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ofinite(c_Set_Oinsert(V_a,V_A,T_a),T_a) ),
file('theBenchmark.p',cls_finite__insert_1) ).
cnf(cls_finite__insert_0,axiom,
( ~ c_Finite__Set_Ofinite(c_Set_Oinsert(V_a,V_A,T_a),T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ),
file('theBenchmark.p',cls_finite__insert_0) ).
cnf(cls_subset__insertI_0,axiom,
c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_subset__insertI_0) ).
cnf(cls_Suc__diff__le_0,axiom,
( ~ c_lessequals(V_n,V_m,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)) ),
file('theBenchmark.p',cls_Suc__diff__le_0) ).
cnf(cls_insert__code_0,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x))
| V_y = V_x
| hBOOL(hAPP(V_A,V_x)) ),
file('theBenchmark.p',cls_insert__code_0) ).
cnf(cls_insert__absorb2_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a),
file('theBenchmark.p',cls_insert__absorb2_0) ).
cnf(cls_subset__insertI2_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_b,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insertI2_0) ).
cnf(cls_insert__subset_1,axiom,
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_insert__subset_1) ).
cnf(cls_finite__surj_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool))
| c_Finite__Set_Ofinite(V_B,T_b) ),
file('theBenchmark.p',cls_finite__surj_0) ).
cnf(cls_image__subset__iff_0,axiom,
( ~ c_lessequals(c_Set_Oimage(V_f,V_A,T_b,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_in(V_x,V_A,T_b)
| c_in(hAPP(V_f,V_x),V_B,T_a) ),
file('theBenchmark.p',cls_image__subset__iff_0) ).
cnf(cls_insert__iff_1,axiom,
c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a),
file('theBenchmark.p',cls_insert__iff_1) ).
cnf(cls_insertI1_0,axiom,
c_in(V_a,c_Set_Oinsert(V_a,V_B,T_a),T_a),
file('theBenchmark.p',cls_insertI1_0) ).
cnf(cls_insertCI_1,axiom,
c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
file('theBenchmark.p',cls_insertCI_1) ).
cnf(cls_insert__commute_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a),
file('theBenchmark.p',cls_insert__commute_0) ).
cnf(cls_mem__def_1,axiom,
( ~ hBOOL(hAPP(V_S,V_x))
| c_in(V_x,V_S,T_a) ),
file('theBenchmark.p',cls_mem__def_1) ).
cnf(cls_mem__def_0,axiom,
( ~ c_in(V_x,V_S,T_a)
| hBOOL(hAPP(V_S,V_x)) ),
file('theBenchmark.p',cls_mem__def_0) ).
cnf(cls_card__insert__if_1,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_in(V_x,V_A,T_a)
| c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a)) ),
file('theBenchmark.p',cls_card__insert__if_1) ).
cnf(cls_diff__le__mono2_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_diff__le__mono2_0) ).
cnf(cls_diff__le__mono_0,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_l,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_l,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_diff__le__mono_0) ).
cnf(cls_le__diff__iff_1,axiom,
( ~ c_lessequals(V_k,V_m,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_le__diff__iff_1) ).
cnf(cls_le__diff__iff_0,axiom,
( ~ c_lessequals(V_k,V_m,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_le__diff__iff_0) ).
cnf(cls_eq__eqI_1,axiom,
( V_xa = V_y
| c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_eq__eqI_1) ).
cnf(cls_eq__eqI_0,axiom,
( V_x_H = V_y_H
| c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('theBenchmark.p',cls_eq__eqI_0) ).
cnf(cls_eq__diff__iff_0,axiom,
( V_m = V_n
| ~ c_lessequals(V_k,V_m,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat) != c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat) ),
file('theBenchmark.p',cls_eq__diff__iff_0) ).
cnf(cls_diff__le__self_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat),
file('theBenchmark.p',cls_diff__le__self_0) ).
cnf(cls_Nat_Odiff__diff__eq_0,axiom,
( ~ c_lessequals(V_k,V_m,tc_nat)
| ~ c_lessequals(V_k,V_n,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
cnf(cls_diff__commute_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat),
file('theBenchmark.p',cls_diff__commute_0) ).
cnf(cls_insert__subset_0,axiom,
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| c_in(V_x,V_B,T_a) ),
file('theBenchmark.p',cls_insert__subset_0) ).
cnf(cls_not__less__eq__eq_1,axiom,
( ~ c_lessequals(c_Suc(V_n),V_m,tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ),
file('theBenchmark.p',cls_not__less__eq__eq_1) ).
cnf(cls_not__less__eq__eq_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(c_Suc(V_n),V_m,tc_nat) ),
file('theBenchmark.p',cls_not__less__eq__eq_0) ).
cnf(cls_insert__code_2,axiom,
( ~ hBOOL(hAPP(V_A,V_x))
| hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x)) ),
file('theBenchmark.p',cls_insert__code_2) ).
cnf(cls_insert__image_0,axiom,
( ~ c_in(V_x,V_A,T_a)
| c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b) ),
file('theBenchmark.p',cls_insert__image_0) ).
cnf(cls_subset__insert__iff_2,axiom,
( c_in(V_x,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insert__iff_2) ).
cnf(cls_subset__insert__iff_1,axiom,
( ~ c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| c_in(V_x,V_A,T_a)
| c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insert__iff_1) ).
cnf(cls_subset__insert_1,axiom,
( c_in(V_x,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insert_1) ).
cnf(cls_subset__insert_0,axiom,
( c_in(V_x,V_A,T_a)
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_subset__insert_0) ).
cnf(cls_insert__ident_0,axiom,
( V_A = V_B
| c_in(V_x,V_A,T_a)
| c_in(V_x,V_B,T_a)
| c_Set_Oinsert(V_x,V_A,T_a) != c_Set_Oinsert(V_x,V_B,T_a) ),
file('theBenchmark.p',cls_insert__ident_0) ).
cnf(cls_Suc__diff__diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat),c_Suc(V_k),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat),
file('theBenchmark.p',cls_Suc__diff__diff_0) ).
cnf(cls_insert__absorb_0,axiom,
( ~ c_in(V_a,V_A,T_a)
| c_Set_Oinsert(V_a,V_A,T_a) = V_A ),
file('theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_le__Suc__eq_2,axiom,
c_lessequals(c_Suc(V_n),c_Suc(V_n),tc_nat),
file('theBenchmark.p',cls_le__Suc__eq_2) ).
cnf(cls_card__mono_0,axiom,
( ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ),
file('theBenchmark.p',cls_card__mono_0) ).
cnf(cls_card__image__le_0,axiom,
( ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(V_f,V_A,T_a,T_b),T_b),c_Finite__Set_Ocard(V_A,T_a),tc_nat) ),
file('theBenchmark.p',cls_card__image__le_0) ).
cnf(cls_finite_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ class_Finite__Set_Ofinite_Ofinite(T_a) ),
file('theBenchmark.p',cls_finite_0) ).
cnf(cls_diff__diff__cancel_0,axiom,
( ~ c_lessequals(V_i,V_n,tc_nat)
| c_HOL_Ominus__class_Ominus(V_n,c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = V_i ),
file('theBenchmark.p',cls_diff__diff__cancel_0) ).
cnf(cls_le__SucE_0,axiom,
( ~ c_lessequals(V_m,c_Suc(V_n),tc_nat)
| c_lessequals(V_m,V_n,tc_nat)
| V_m = c_Suc(V_n) ),
file('theBenchmark.p',cls_le__SucE_0) ).
cnf(cls_rev__image__eqI_0,axiom,
( c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_aa,T_a),T_a)
| ~ c_in(V_x,V_A,T_aa) ),
file('theBenchmark.p',cls_rev__image__eqI_0) ).
cnf(cls_image__iff_2,axiom,
( c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_b,T_a),T_a)
| ~ c_in(V_x,V_A,T_b) ),
file('theBenchmark.p',cls_image__iff_2) ).
cnf(cls_image__eqI_0,axiom,
( ~ c_in(V_x,V_A,T_b)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_b,T_a),T_a) ),
file('theBenchmark.p',cls_image__eqI_0) ).
cnf(cls_imageI_0,axiom,
( ~ c_in(V_x,V_A,T_a)
| c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) ),
file('theBenchmark.p',cls_imageI_0) ).
cnf(cls_le__funD_0,axiom,
( ~ c_lessequals(V_f,V_g,tc_fun(T_a,T_b))
| c_lessequals(hAPP(V_f,V_x),hAPP(V_g,V_x),T_b)
| ~ class_HOL_Oord(T_b) ),
file('theBenchmark.p',cls_le__funD_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_3,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_4,negated_conjecture,
c_in(v_pn,v_U,tc_Com_Opname),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(cls_conjecture_6,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(clsarity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_1)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
cnf(clsarity_fun__Lattices_Olower__semilattice,axiom,
( ~ class_Lattices_Olattice(T_1)
| class_Lattices_Olower__semilattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
cnf(clsarity_fun__Lattices_Obounded__lattice,axiom,
( ~ class_Lattices_Obounded__lattice(T_1)
| class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
cnf(clsarity_fun__Finite__Set_Ofinite_Ofinite,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(T_2)
| ~ class_Finite__Set_Ofinite_Ofinite(T_1)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
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__Lattices_Olattice,axiom,
( ~ class_Lattices_Olattice(T_1)
| class_Lattices_Olattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
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_fun__Orderings_Otop,axiom,
( ~ class_Orderings_Otop(T_1)
| class_Orderings_Otop(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Orderings_Otop) ).
cnf(clsarity_fun__Orderings_Obot,axiom,
( ~ class_Orderings_Obot(T_1)
| class_Orderings_Obot(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Orderings_Obot) ).
cnf(clsarity_fun__HOL_Oord,axiom,
( ~ class_HOL_Oord(T_1)
| class_HOL_Oord(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__HOL_Oord) ).
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__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
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_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
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__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
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__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
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__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
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_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
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__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
cnf(clsarity_nat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_nat),
file('theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
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__Ring__and__Field_Odvd,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
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__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_nat),
file('theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
file('theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat),
file('theBenchmark.p',clsarity_nat__Orderings_Obot) ).
cnf(clsarity_nat__HOL_Oord,axiom,
class_HOL_Oord(tc_nat),
file('theBenchmark.p',clsarity_nat__HOL_Oord) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('theBenchmark.p',clsarity_bool__Orderings_Otop) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('theBenchmark.p',clsarity_bool__HOL_Oord) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
c_fequal(V_x,V_x,T_a),
file('theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( ~ c_fequal(V_X,V_Y,T_a)
| V_X = V_Y ),
file('theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
cnf(cls_add__nonneg__eq__0__iff_2_simplified,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),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_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_6,axiom,
( c_HOL_Otimes__class_Otimes(Eq_x_0,Eq_x_1,Eq_x_2) = c_HOL_Otimes__class_Otimes(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_Suc(Eq_x_0) = c_Suc(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( c_HOL_Oplus__class_Oplus(Eq_x_0,Eq_x_1,Eq_x_2) = c_HOL_Oplus__class_Oplus(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_9,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_10,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lattices_Olower__semilattice__class_Oinf(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_11,axiom,
( c_Orderings_Obot__class_Obot(Eq_x_0) = c_Orderings_Obot__class_Obot(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( c_HOL_Ominus__class_Ominus(Eq_x_0,Eq_x_1,Eq_x_2) = c_HOL_Ominus__class_Ominus(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_Divides_Odiv__class_Omod(Eq_x_0,Eq_x_1,Eq_x_2) = c_Divides_Odiv__class_Omod(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_14,axiom,
( c_Set_Ovimage(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Set_Ovimage(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_15,axiom,
( c_Orderings_Otop__class_Otop(Eq_x_0) = c_Orderings_Otop__class_Otop(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,axiom,
( c_Set_Oinsert(Eq_x_0,Eq_x_1,Eq_x_2) = c_Set_Oinsert(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_18,axiom,
( c_Set_Oimage(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Set_Oimage(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_19,axiom,
( c_Hilbert__Choice_Oinv__into(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Hilbert__Choice_Oinv__into(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_20,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_21,axiom,
( c_Finite__Set_Ocard(Eq_x_0,Eq_x_1) = c_Finite__Set_Ocard(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2(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_23,axiom,
( c_Finite__Set_Olinorder__class_OMax(Eq_x_0,Eq_x_1) = c_Finite__Set_Olinorder__class_OMax(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(Eq_x_0) = c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2(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_26,axiom,
( c_Fun_Ofun__upd(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Fun_Ofun__upd(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_27,axiom,
( c_Finite__Set_Olinorder__class_OMin(Eq_x_0,Eq_x_1) = c_Finite__Set_Olinorder__class_OMin(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(Eq_x_0,Eq_x_1) = c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( c_Inductive_Ocomplete__lattice__class_Ogfp(Eq_x_0,Eq_x_1) = c_Inductive_Ocomplete__lattice__class_Ogfp(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( c_SetInterval_Oord__class_OatLeast(Eq_x_0,Eq_x_1) = c_SetInterval_Oord__class_OatLeast(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(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_32,axiom,
( c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(Eq_x_0) = c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( c_ATP__Linkup_Osko__Set__XimageE__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_ATP__Linkup_Osko__Set__XimageE__1__1(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_34,axiom,
( c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(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_35,axiom,
( c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(Eq_x_0) = c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(Eq_x_0,Eq_x_1) = c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1(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_38,axiom,
( c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(Eq_x_0,Eq_x_1) = c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1(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_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1(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_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1(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_42,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_43,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(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_44,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_45,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_46,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_47,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_48,axiom,
( class_Divides_Osemiring__div(Eq_y_0)
| ~ class_Divides_Osemiring__div(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( c_Finite__Set_Ofinite(Eq_y_0,Eq_y_1)
| ~ c_Finite__Set_Ofinite(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( c_Fun_Oinj__on(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ c_Fun_Oinj__on(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_51,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_52,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_53,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_54,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_55,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_56,axiom,
( class_OrderedGroup_Olordered__ab__group__add__meet(Eq_y_0)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_57,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_58,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_59,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_60,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_61,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_62,axiom,
( class_Ring__and__Field_Odvd(Eq_y_0)
| ~ class_Ring__and__Field_Odvd(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_63,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_64,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(Eq_y_0)
| ~ class_OrderedGroup_Ocomm__monoid__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_65,axiom,
( c_in(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_in(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_66,axiom,
( class_Ring__and__Field_Oring(Eq_y_0)
| ~ class_Ring__and__Field_Oring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_67,axiom,
( class_Ring__and__Field_Oordered__semiring__strict(Eq_y_0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_68,axiom,
( class_Ring__and__Field_Oordered__ring__strict(Eq_y_0)
| ~ class_Ring__and__Field_Oordered__ring__strict(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_69,axiom,
( class_Lattices_Obounded__lattice(Eq_y_0)
| ~ class_Lattices_Obounded__lattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_70,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_71,axiom,
( class_Ring__and__Field_Oordered__semiring(Eq_y_0)
| ~ class_Ring__and__Field_Oordered__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_72,axiom,
( class_Ring__and__Field_Opordered__ring(Eq_y_0)
| ~ class_Ring__and__Field_Opordered__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_73,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_74,axiom,
( class_Lattices_Olower__semilattice(Eq_y_0)
| ~ class_Lattices_Olower__semilattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_75,axiom,
( class_Lattices_Olattice(Eq_y_0)
| ~ class_Lattices_Olattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_76,axiom,
( class_Ring__and__Field_Osemiring(Eq_y_0)
| ~ class_Ring__and__Field_Osemiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_77,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(Eq_y_0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_78,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_79,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_80,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_81,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_82,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_83,axiom,
( class_Ring__and__Field_Oordered__comm__semiring__strict(Eq_y_0)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_84,axiom,
( class_Ring__and__Field_Oring__no__zero__divisors(Eq_y_0)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_85,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_86,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_87,axiom,
( class_Ring__and__Field_Opordered__semiring(Eq_y_0)
| ~ class_Ring__and__Field_Opordered__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_88,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_89,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_90,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_91,axiom,
( class_Complete__Lattice_Ocomplete__lattice(Eq_y_0)
| ~ class_Complete__Lattice_Ocomplete__lattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_92,axiom,
( class_Orderings_Otop(Eq_y_0)
| ~ class_Orderings_Otop(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_93,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_94,axiom,
( class_OrderedGroup_Oab__semigroup__idem__mult(Eq_y_0)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_95,axiom,
( class_Ring__and__Field_Omult__mono(Eq_y_0)
| ~ class_Ring__and__Field_Omult__mono(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_96,axiom,
( class_Ring__and__Field_Omult__mono1(Eq_y_0)
| ~ class_Ring__and__Field_Omult__mono1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_97,axiom,
( class_Orderings_Obot(Eq_y_0)
| ~ class_Orderings_Obot(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_98,axiom,
( class_Divides_Oring__div(Eq_y_0)
| ~ class_Divides_Oring__div(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_99,axiom,
( class_Ring__and__Field_Ocomm__ring__1(Eq_y_0)
| ~ class_Ring__and__Field_Ocomm__ring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_100,axiom,
( class_OrderedGroup_Ogroup__add(Eq_y_0)
| ~ class_OrderedGroup_Ogroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_101,axiom,
( class_Finite__Set_Ofinite_Ofinite(Eq_y_0)
| ~ class_Finite__Set_Ofinite_Ofinite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_102,axiom,
( class_HOL_Oord(Eq_y_0)
| ~ class_HOL_Oord(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_103,axiom,
( class_Ring__and__Field_Ocomm__ring(Eq_y_0)
| ~ class_Ring__and__Field_Ocomm__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_104,axiom,
( class_OrderedGroup_Oab__semigroup__mult(Eq_y_0)
| ~ class_OrderedGroup_Oab__semigroup__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_105,axiom,
( class_Ring__and__Field_Ocomm__semiring(Eq_y_0)
| ~ class_Ring__and__Field_Ocomm__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_106,axiom,
( class_Ring__and__Field_Oring__1(Eq_y_0)
| ~ class_Ring__and__Field_Oring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_107,axiom,
( c_fequal(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_fequal(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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV884-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n007.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 : Sun Sep 20 04:49:35 UTC 2026
% 0.09/0.37 % CPUTime :
% 150.16/150.45 % SZS status Unsatisfiable for theBenchmark
% 150.16/150.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------