%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SCT080-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:55:27 AM UTC 2026
% Result : Unsatisfiable 72.03s 82.39s
% Output : Proof 72.23s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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_Un__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_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_D,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__mono_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_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_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__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__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__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_subset__Un__eq_1,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) != V_B ),
file('theBenchmark.p',cls_subset__Un__eq_1) ).
cnf(cls_Un__absorb2_0,axiom,
( ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = V_A ),
file('theBenchmark.p',cls_Un__absorb2_0) ).
cnf(cls_Un__absorb1_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = V_B ),
file('theBenchmark.p',cls_Un__absorb1_0) ).
cnf(cls_le__iff__sup_0,axiom,
( ~ c_lessequals(V_x,V_y,T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__iff__sup_0) ).
cnf(cls_le__iff__sup_1,axiom,
( c_lessequals(V_x,V_y,T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) != V_y
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__iff__sup_1) ).
cnf(cls_sup__absorb1_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_x
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__absorb1_0) ).
cnf(cls_inf__sup__absorb_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = V_x
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__absorb_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_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_sup__inf__absorb_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = V_x
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_sup__inf__absorb_0) ).
cnf(cls_distrib__sup__le_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_distrib__sup__le_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_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_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_Un__empty__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(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_Un__empty__right_0) ).
cnf(cls_Un__empty__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B,
file('theBenchmark.p',cls_Un__empty__left_0) ).
cnf(cls_sup__bot__left_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) = V_x
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_sup__bot__left_0) ).
cnf(cls_sup__bot__right_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Orderings_Obot__class_Obot(T_a),T_a) = V_x
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_sup__bot__right_0) ).
cnf(cls_sup1CI_1,axiom,
( ~ hBOOL(hAPP(V_A,V_x))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ),
file('theBenchmark.p',cls_sup1CI_1) ).
cnf(cls_sup1CI_0,axiom,
( ~ hBOOL(hAPP(V_B,V_x))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ),
file('theBenchmark.p',cls_sup1CI_0) ).
cnf(cls_sup1E_0,axiom,
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
| hBOOL(hAPP(V_A,V_x))
| hBOOL(hAPP(V_B,V_x)) ),
file('theBenchmark.p',cls_sup1E_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_Un__Int__assoc__eq_1,axiom,
( ~ c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(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_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
cnf(cls_Un__Int__assoc__eq_0,axiom,
( c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(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_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
cnf(cls_Image__Int__subset_0,axiom,
c_lessequals(c_Relation_OImage(V_R,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_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,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_empty__fold__graphE_0,axiom,
( ~ c_Finite__Set_Ofold__graph(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x,T_a,T_b)
| V_x = V_z ),
file('theBenchmark.p',cls_empty__fold__graphE_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_Image__empty_0,axiom,
c_Relation_OImage(V_R,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_Un__UNIV__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__UNIV__right_0) ).
cnf(cls_Un__UNIV__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__UNIV__left_0) ).
cnf(cls_sup__top__left_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(T_a),V_x,T_a) = c_Orderings_Otop__class_Otop(T_a)
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_sup__top__left_0) ).
cnf(cls_sup__top__right_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Orderings_Otop__class_Otop(T_a),T_a) = c_Orderings_Otop__class_Otop(T_a)
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_sup__top__right_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_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__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__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_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_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_sup__inf__distrib2_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_z,V_x,T_a),T_a)
| ~ class_Lattices_Odistrib__lattice(T_a) ),
file('theBenchmark.p',cls_sup__inf__distrib2_0) ).
cnf(cls_sup__inf__distrib1_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Odistrib__lattice(T_a) ),
file('theBenchmark.p',cls_sup__inf__distrib1_0) ).
cnf(cls_Un__Int__distrib_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(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(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__Int__distrib_0) ).
cnf(cls_Un__Int__distrib2_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__Int__distrib2_0) ).
cnf(cls_image__image_0,axiom,
c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_A,T_c,T_b),T_b,T_a) = c_Set_Oimage(c_COMBB(V_f,V_g,T_b,T_a,T_c),V_A,T_c,T_a),
file('theBenchmark.p',cls_image__image_0) ).
cnf(cls_le__sup__iff_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a)
| c_lessequals(V_y,V_z,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__sup__iff_1) ).
cnf(cls_le__sup__iff_0,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__sup__iff_0) ).
cnf(cls_le__supI2_0,axiom,
( ~ c_lessequals(V_x,V_b,T_a)
| c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__supI2_0) ).
cnf(cls_le__supI1_0,axiom,
( ~ c_lessequals(V_x,V_a,T_a)
| c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__supI1_0) ).
cnf(cls_le__supE_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a)
| c_lessequals(V_b,V_x,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__supE_1) ).
cnf(cls_le__supE_0,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a)
| c_lessequals(V_a,V_x,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__supE_0) ).
cnf(cls_Un__subset__iff_0,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__subset__iff_0) ).
cnf(cls_Un__subset__iff_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool))
| c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__subset__iff_1) ).
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_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_equalityE_0,axiom,
c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_equalityE_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__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__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_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_order__eq__iff_0,axiom,
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('theBenchmark.p',cls_order__eq__iff_0) ).
cnf(cls_order__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_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_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_lfp__lowerbound_0,axiom,
( ~ c_lessequals(hAPP(V_f,V_A),V_A,T_a)
| c_lessequals(c_Inductive_Ocomplete__lattice__class_Olfp(V_f,T_a),V_A,T_a)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_lfp__lowerbound_0) ).
cnf(cls_UN__Un_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),V_M,T_b,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_M,T_b,tc_fun(T_a,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_B,V_M,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_UN__Un_0) ).
cnf(cls_inj__transfer_1,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| ~ hBOOL(hAPP(V_P,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(V_P,V_f,T_a,T_b))))
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_inj__transfer_1) ).
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_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_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_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_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_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_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_Un__empty_2,axiom,
c_Lattices_Oupper__semilattice__class_Osup(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)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__empty_2) ).
cnf(cls_image__Un_0,axiom,
c_Set_Oimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(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)),
file('theBenchmark.p',cls_image__Un_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_equiv__class__self_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a))) ),
file('theBenchmark.p',cls_equiv__class__self_0) ).
cnf(cls_subset__equiv__class_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ c_lessequals(c_Relation_OImage(V_r,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a),c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a),tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),V_A))
| hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),V_r)) ),
file('theBenchmark.p',cls_subset__equiv__class_0) ).
cnf(cls_fold__graph_OinsertI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Finite__Set_Ofold__graph(V_f,V_z,V_A,V_y,T_a,T_b)
| c_Finite__Set_Ofold__graph(V_f,V_z,c_Set_Oinsert(V_x,V_A,T_a),hAPP(hAPP(V_f,V_x),V_y),T_a,T_b) ),
file('theBenchmark.p',cls_fold__graph_OinsertI_0) ).
cnf(cls_subset__insert_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_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_subset__insert_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_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__iff_1,axiom,
( ~ c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_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__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_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_insert__subset_0,axiom,
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ),
file('theBenchmark.p',cls_insert__subset_0) ).
cnf(cls_insert__subset_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ 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_inv__into__into_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oimage(V_f,V_A,T_b,T_a)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_b,T_a),V_x)),V_A)) ),
file('theBenchmark.p',cls_inv__into__into_0) ).
cnf(cls_inv__into__injective_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),c_Set_Oimage(V_f,V_A,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_y),c_Set_Oimage(V_f,V_A,T_a,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_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))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),V_B)) ),
file('theBenchmark.p',cls_image__subset__iff_0) ).
cnf(cls_f__inv__into__f_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),c_Set_Oimage(V_f,V_A,T_b,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_fun__upd__image_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| 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_equiv__class__eq_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),V_r))
| c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) = c_Relation_OImage(V_r,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) ),
file('theBenchmark.p',cls_equiv__class__eq_0) ).
cnf(cls_equiv__class__eq__iff_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))
| c_Relation_OImage(V_r,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) = c_Relation_OImage(V_r,c_Set_Oinsert(V_y,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) ),
file('theBenchmark.p',cls_equiv__class__eq__iff_0) ).
cnf(cls_le__SUPI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),V_A))
| c_lessequals(hAPP(V_M,V_i),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_M,T_a,T_b),T_b)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
file('theBenchmark.p',cls_le__SUPI_0) ).
cnf(cls_UN__upper_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| c_lessequals(hAPP(V_B,V_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_UN__upper_0) ).
cnf(cls_UN__subset__iff_0,axiom,
( ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_b,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_I))
| c_lessequals(hAPP(V_A,V_x),V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_UN__subset__iff_0) ).
cnf(cls_UN__absorb_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_k),V_I))
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(V_A,V_k),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_a,tc_fun(T_b,tc_bool)),tc_fun(T_b,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_a,tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_UN__absorb_0) ).
cnf(cls_pred__subset__eq_0,axiom,
( ~ c_lessequals(hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_R),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_S),tc_fun(T_a,tc_bool))
| c_lessequals(V_R,V_S,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_pred__subset__eq_0) ).
cnf(cls_pred__subset__eq_1,axiom,
( ~ c_lessequals(V_R,V_S,tc_fun(T_a,tc_bool))
| c_lessequals(hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_R),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_S),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_pred__subset__eq_1) ).
cnf(cls_inv__into__f__f_0,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_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)
| ~ hBOOL(hAPP(hAPP(c_in(T_aa),V_x),V_A)) ),
file('theBenchmark.p',cls_inv__into__f__eq_0) ).
cnf(cls_Sup__upper_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| c_lessequals(V_x,c_Complete__Lattice_OSup__class_OSup(V_A,T_a),T_a)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_Sup__upper_0) ).
cnf(cls_insert__is__Un_0,axiom,
c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_insert__is__Un_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_UN__extend__simps_I2_J_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_A,T_b,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B,
file('theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
cnf(cls_UN__extend__simps_I3_J_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A,
file('theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
cnf(cls_UN__insert_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(V_a,V_A,T_b),V_B,T_b,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(V_B,V_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_UN__insert_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_range__composition_0,axiom,
c_Set_Oimage(c_COMBB(V_f,V_g,T_c,T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Set_Oimage(V_f,c_Set_Oimage(V_g,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_c),T_c,T_a),
file('theBenchmark.p',cls_range__composition_0) ).
cnf(cls_UN__extend__simps_I10_J_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(V_B,V_f,T_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(V_f,V_A,T_b,T_c),V_B,T_c,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_UN__extend__simps_I10_J_0) ).
cnf(cls_UN__simps_I10_J_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(V_f,V_A,T_c,T_b),V_B,T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(V_B,V_f,T_b,tc_fun(T_a,tc_bool),T_c),T_c,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_UN__simps_I10_J_0) ).
cnf(cls_Sup__insert_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(V_a,V_A,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_a,c_Complete__Lattice_OSup__class_OSup(V_A,T_a),T_a)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_Sup__insert_0) ).
cnf(cls_inj__on__Un__image__eq__iff_0,axiom,
( V_A = V_B
| ~ c_Fun_Oinj__on(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,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__on__Un__image__eq__iff_0) ).
cnf(cls_Union__upper_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_B),V_A))
| c_lessequals(V_B,c_Complete__Lattice_OSup__class_OSup(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Union__upper_0) ).
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_Un__Diff__Int_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(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)),tc_fun(T_a,tc_bool)) = V_A,
file('theBenchmark.p',cls_Un__Diff__Int_0) ).
cnf(cls_Diff__Un_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__Un_0) ).
cnf(cls_Diff__Int_0,axiom,
c_HOL_Ominus__class_Ominus(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_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Diff__Int_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_Inf__lower_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(V_A,T_a),V_x,T_a)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_Inf__lower_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_PowD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_A),c_Set_OPow(V_B,T_a)))
| c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_PowD_0) ).
cnf(cls_PowI_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_A),c_Set_OPow(V_B,T_a))) ),
file('theBenchmark.p',cls_PowI_0) ).
cnf(cls_Union__quotient_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(V_A,V_r,T_a),tc_fun(T_a,tc_bool)) = V_A ),
file('theBenchmark.p',cls_Union__quotient_0) ).
cnf(cls_Inter__lower_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_B),V_A))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(V_A,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Inter__lower_0) ).
cnf(cls_eq__equiv__class__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))
| ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))
| c_Relation_OImage(V_r,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) != c_Relation_OImage(V_r,c_Set_Oinsert(V_y,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) ),
file('theBenchmark.p',cls_eq__equiv__class__iff_0) ).
cnf(cls_eq__equiv__class__iff_1,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))
| c_Relation_OImage(V_r,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) = c_Relation_OImage(V_r,c_Set_Oinsert(V_y,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) ),
file('theBenchmark.p',cls_eq__equiv__class__iff_1) ).
cnf(cls_equiv__class__eq__iff_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))
| hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))
| ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| c_Relation_OImage(V_r,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) != c_Relation_OImage(V_r,c_Set_Oinsert(V_y,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) ),
file('theBenchmark.p',cls_equiv__class__eq__iff_3) ).
cnf(cls_eq__equiv__class_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),V_A))
| hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),V_r))
| c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) != c_Relation_OImage(V_r,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) ),
file('theBenchmark.p',cls_eq__equiv__class_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))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_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))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_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))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_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_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_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_Un__insert__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_Un__insert__right_0) ).
cnf(cls_Un__insert__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_Un__insert__left_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_Int__Un__distrib2_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Int__Un__distrib2_0) ).
cnf(cls_Int__Un__distrib_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),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__Un__distrib_0) ).
cnf(cls_inf__sup__distrib1_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Odistrib__lattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__distrib1_0) ).
cnf(cls_inf__sup__distrib2_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_z,V_x,T_a),T_a)
| ~ class_Lattices_Odistrib__lattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__distrib2_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_Un__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A,
file('theBenchmark.p',cls_Un__absorb_0) ).
cnf(cls_sup__idem_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_x,T_a) = V_x
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__idem_0) ).
cnf(cls_Image__Un_0,axiom,
c_Relation_OImage(V_R,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Image__Un_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R)),
file('theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_Un__left__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__left__commute_0) ).
cnf(cls_Un__assoc_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__assoc_0) ).
cnf(cls_sup__assoc_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__assoc_0) ).
cnf(cls_sup__left__commute_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__left__commute_0) ).
cnf(cls_inf__sup__aci_I7_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
cnf(cls_inf__sup__aci_I6_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I6_J_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_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_Un__subset__iff_2,axiom,
( ~ 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_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__subset__iff_2) ).
cnf(cls_Un__upper2_0,axiom,
c_lessequals(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__upper2_0) ).
cnf(cls_Un__upper1_0,axiom,
c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__upper1_0) ).
cnf(cls_Un__least_0,axiom,
( ~ 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_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Un__least_0) ).
cnf(cls_le__supI_0,axiom,
( ~ c_lessequals(V_a,V_x,T_a)
| ~ c_lessequals(V_b,V_x,T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__supI_0) ).
cnf(cls_sup__ge1_0,axiom,
( c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__ge1_0) ).
cnf(cls_sup__ge2_0,axiom,
( c_lessequals(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__ge2_0) ).
cnf(cls_sup__least_0,axiom,
( ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_z,V_x,T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__least_0) ).
cnf(cls_le__sup__iff_2,axiom,
( ~ c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_le__sup__iff_2) ).
cnf(cls_inf__sup__ord_I4_J_0,axiom,
( c_lessequals(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
cnf(cls_inf__sup__ord_I3_J_0,axiom,
( c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
cnf(cls_Diff__partition_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_B ),
file('theBenchmark.p',cls_Diff__partition_0) ).
cnf(cls_equiv__class__subset_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),V_r))
| c_lessequals(c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a),c_Relation_OImage(V_r,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_equiv__class__subset_0) ).
cnf(cls_distrib__inf__le_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a),T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_distrib__inf__le_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_Un__Int__crazy_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(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_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__Int__crazy_0) ).
cnf(cls_fold__graph_OemptyI_0,axiom,
c_Finite__Set_Ofold__graph(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_z,T_a,T_b),
file('theBenchmark.p',cls_fold__graph_OemptyI_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_Un__empty_1,axiom,
( V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(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_Un__empty_1) ).
cnf(cls_Un__empty_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(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_Un__empty_0) ).
cnf(cls_sup__eq__bot__eq1_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,T_a) != c_Orderings_Obot__class_Obot(T_a)
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
cnf(cls_sup__eq__bot__eq2_0,axiom,
( V_B = c_Orderings_Obot__class_Obot(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,T_a) != c_Orderings_Obot__class_Obot(T_a)
| ~ class_Lattices_Obounded__lattice(T_a) ),
file('theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
cnf(cls_Un__Diff__cancel2_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__Diff__cancel2_0) ).
cnf(cls_Un__Diff__cancel_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__Diff__cancel_0) ).
cnf(cls_bij__betw__inv__into_0,axiom,
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Obij__betw(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),V_B,V_A,T_b,T_a) ),
file('theBenchmark.p',cls_bij__betw__inv__into_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_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_Un__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),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_Un__Diff_0) ).
cnf(cls_Un__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__commute_0) ).
cnf(cls_sup__commute_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__commute_0) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
cnf(cls_Un__left__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_Un__left__absorb_0) ).
cnf(cls_sup__left__idem_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a)
| ~ class_Lattices_Oupper__semilattice(T_a) ),
file('theBenchmark.p',cls_sup__left__idem_0) ).
cnf(cls_inf__sup__aci_I8_J_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a)
| ~ class_Lattices_Olattice(T_a) ),
file('theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
cnf(cls_vimage__Un_0,axiom,
c_Set_Ovimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(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__Un_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_inj__on__Un_1,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b)
| c_Fun_Oinj__on(V_f,V_B,T_a,T_b) ),
file('theBenchmark.p',cls_inj__on__Un_1) ).
cnf(cls_inj__on__Un_0,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ),
file('theBenchmark.p',cls_inj__on__Un_0) ).
cnf(cls_Diff__subset__conv_1,axiom,
( ~ c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Diff__subset__conv_1) ).
cnf(cls_Diff__subset__conv_0,axiom,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool))
| c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Diff__subset__conv_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_subset__iff_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B)) ),
file('theBenchmark.p',cls_subset__iff_0) ).
cnf(cls_set__rev__mp_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ),
file('theBenchmark.p',cls_set__rev__mp_0) ).
cnf(cls_subsetD_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B)) ),
file('theBenchmark.p',cls_subsetD_0) ).
cnf(cls_set__mp_0,axiom,
( ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ),
file('theBenchmark.p',cls_set__mp_0) ).
cnf(cls_UnCI_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)))) ),
file('theBenchmark.p',cls_UnCI_1) ).
cnf(cls_UnCI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)))) ),
file('theBenchmark.p',cls_UnCI_0) ).
cnf(cls_UnE_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B)) ),
file('theBenchmark.p',cls_UnE_0) ).
cnf(cls_compose__def_0,axiom,
c_FuncSet_Ocompose(V_A,V_g,V_f,T_a,T_c,T_b) = c_FuncSet_Orestrict(c_COMBB(V_g,V_f,T_c,T_b,T_a),V_A,T_a,T_b),
file('theBenchmark.p',cls_compose__def_0) ).
cnf(cls_bex__Un_6,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(V_P,V_x))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)))) ),
file('theBenchmark.p',cls_bex__Un_6) ).
cnf(cls_bex__Un_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_A))
| ~ hBOOL(hAPP(V_P,V_xa))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)))) ),
file('theBenchmark.p',cls_bex__Un_4) ).
cnf(cls_rev__ImageI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),V_r))
| hBOOL(hAPP(hAPP(c_in(T_b),V_b),c_Relation_OImage(V_r,V_A,T_a,T_b))) ),
file('theBenchmark.p',cls_rev__ImageI_0) ).
cnf(cls_Image__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_a)),c_Pair(V_x,V_b,T_b,T_a)),V_r))
| hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Relation_OImage(V_r,V_A,T_b,T_a))) ),
file('theBenchmark.p',cls_Image__iff_2) ).
cnf(cls_equiv__class__eq__iff_2,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))
| hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A)) ),
file('theBenchmark.p',cls_equiv__class__eq__iff_2) ).
cnf(cls_equiv__class__eq__iff_1,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ),
file('theBenchmark.p',cls_equiv__class__eq__iff_1) ).
cnf(cls_equiv__class__nondisjoint_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a),c_Relation_OImage(V_r,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a),tc_fun(T_a,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),V_r)) ),
file('theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
cnf(cls_inj__on__fun__updI_0,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| hBOOL(hAPP(hAPP(c_in(T_b),V_y),c_Set_Oimage(V_f,V_A,T_a,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_insert__def_0,axiom,
c_Set_Oinsert(V_a,V_B,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_a),T_a),V_B,tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_insert__def_0) ).
cnf(cls_Sup__binary_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(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),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_Sup__binary_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_Union__disjoint_2,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(V_C,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))
| c_Lattices_Olower__semilattice__class_Oinf(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(V_A,V_C,T_a),V_A,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Union__disjoint_2) ).
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_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_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_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_vimage__insert_0,axiom,
c_Set_Ovimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(V_f,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),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__insert_0) ).
cnf(cls_setsum__diff1__nat_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| c_Finite__Set_Osetsum(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,tc_nat) = c_Finite__Set_Osetsum(V_f,V_A,T_a,tc_nat) ),
file('theBenchmark.p',cls_setsum__diff1__nat_1) ).
cnf(cls_Diff1__fold__graph_0,axiom,
( ~ c_Finite__Set_Ofold__graph(V_f,V_z,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_y,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| c_Finite__Set_Ofold__graph(V_f,V_z,V_A,hAPP(hAPP(V_f,V_x),V_y),T_a,T_b) ),
file('theBenchmark.p',cls_Diff1__fold__graph_0) ).
cnf(cls_range__ex1__eq_2,axiom,
( hAPP(V_f,V_x) = hAPP(V_f,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(hAPP(V_f,V_x),V_f,V_x,T_a,T_aa))
| hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a)))
| ~ 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_range__ex1__eq_2) ).
cnf(cls_inj__transfer_0,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| hBOOL(hAPP(hAPP(c_in(T_b),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(V_P,V_f,T_a,T_b)),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)))
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_inj__transfer_0) ).
cnf(cls_range__ex1__eq_3,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a)))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a)
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(hAPP(V_f,V_x),V_f,V_x,T_a,T_aa) != V_x ),
file('theBenchmark.p',cls_range__ex1__eq_3) ).
cnf(cls_range__ex1__eq_0,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_b),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)))
| V_b = hAPP(V_f,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(V_b,V_f,T_b,T_a)) ),
file('theBenchmark.p',cls_range__ex1__eq_0) ).
cnf(cls_range__ex1__eq_1,axiom,
( V_y = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(hAPP(V_f,V_y),V_f,T_a,T_aa)
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_y)),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a))) ),
file('theBenchmark.p',cls_range__ex1__eq_1) ).
cnf(cls_Union__disjoint_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(V_A,V_C,T_a)),V_C))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(V_C,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_Union__disjoint_1) ).
cnf(cls_vimage__def_0,axiom,
c_Set_Ovimage(V_f,V_B,T_a,T_b) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(T_b),V_f,T_b,tc_fun(tc_fun(T_b,tc_bool),tc_bool),T_a),T_a,tc_fun(T_b,tc_bool),tc_bool),V_B),T_a),
file('theBenchmark.p',cls_vimage__def_0) ).
cnf(cls_quotient__disj_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_X),c_Equiv__Relations_Oquotient(V_A,V_r,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_Y),c_Equiv__Relations_Oquotient(V_A,V_r,T_a)))
| V_X = V_Y
| c_Lattices_Olower__semilattice__class_Oinf(V_X,V_Y,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_quotient__disj_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_funcset__image_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_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)) ),
file('theBenchmark.p',cls_funcset__image_0) ).
cnf(cls_restrictI_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,c_FuncSet_Osko__FuncSet__XrestrictI__1__1(V_A,V_B,V_f,T_a,T_b))),hAPP(V_B,c_FuncSet_Osko__FuncSet__XrestrictI__1__1(V_A,V_B,V_f,T_a,T_b))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(V_f,V_A,T_a,T_b)),c_FuncSet_OPi(V_A,V_B,T_a,T_b))) ),
file('theBenchmark.p',cls_restrictI_1) ).
cnf(cls_restrictI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_FuncSet_Osko__FuncSet__XrestrictI__1__1(V_A,V_B,V_f,T_a,T_b)),V_A))
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(V_f,V_A,T_a,T_b)),c_FuncSet_OPi(V_A,V_B,T_a,T_b))) ),
file('theBenchmark.p',cls_restrictI_0) ).
cnf(cls_compose__id__inv__into_0,axiom,
c_FuncSet_Ocompose(c_Set_Oimage(V_f,V_A,T_b,T_a),V_f,c_FuncSet_Orestrict(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_b,T_a),c_Set_Oimage(V_f,V_A,T_b,T_a),T_a,T_b),T_a,T_b,T_a) = c_FuncSet_Orestrict(c_COMBI(T_a),c_Set_Oimage(V_f,V_A,T_b,T_a),T_a,T_a),
file('theBenchmark.p',cls_compose__id__inv__into_0) ).
cnf(cls_compose__inv__into__id_0,axiom,
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_FuncSet_Ocompose(V_A,c_FuncSet_Orestrict(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),V_B,T_b,T_a),V_f,T_a,T_b,T_a) = c_FuncSet_Orestrict(c_COMBI(T_a),V_A,T_a,T_a) ),
file('theBenchmark.p',cls_compose__inv__into__id_0) ).
cnf(cls_Image__singleton__iff_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),T_b,T_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_a)),c_Pair(V_a,V_b,T_b,T_a)),V_r)) ),
file('theBenchmark.p',cls_Image__singleton__iff_0) ).
cnf(cls_Image__singleton__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_a)),c_Pair(V_a,V_b,T_b,T_a)),V_r))
| hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),T_b,T_a))) ),
file('theBenchmark.p',cls_Image__singleton__iff_1) ).
cnf(cls_fun__upd__image_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| 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_quotient__eq__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_xa,V_y,T_a,T_a)),V_r))
| ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_x),c_Equiv__Relations_Oquotient(V_A,V_r,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_x),c_Equiv__Relations_Oquotient(V_A,V_r,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_x)) ),
file('theBenchmark.p',cls_quotient__eq__iff_0) ).
cnf(cls_quotient__eqI_0,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_X),c_Equiv__Relations_Oquotient(V_A,V_r,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_Y),c_Equiv__Relations_Oquotient(V_A,V_r,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_X))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_Y))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))
| V_X = V_Y ),
file('theBenchmark.p',cls_quotient__eqI_0) ).
cnf(cls_quotientI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),c_Relation_OImage(V_r,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a)),c_Equiv__Relations_Oquotient(V_A,V_r,T_a))) ),
file('theBenchmark.p',cls_quotientI_0) ).
cnf(cls_inj__on__Un_2,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Lattices_Oupper__semilattice__class_Osup(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,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),T_a,T_b),tc_fun(T_b,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_inj__on__Un_2) ).
cnf(cls_inj__on__Un_3,axiom,
( c_Fun_Oinj__on(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,V_B,T_a,T_b)
| c_Lattices_Olower__semilattice__class_Oinf(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_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),T_a,T_b),tc_fun(T_b,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ),
file('theBenchmark.p',cls_inj__on__Un_3) ).
cnf(cls_inv__into__funcset_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_b,T_a),c_Set_Oimage(V_f,V_A,T_b,T_a),T_a,T_b)),c_FuncSet_OPi(c_Set_Oimage(V_f,V_A,T_b,T_a),c_COMBK(V_A,tc_fun(T_b,tc_bool),T_a),T_a,T_b))),
file('theBenchmark.p',cls_inv__into__funcset_0) ).
cnf(cls_1_0,axiom,
( V_a = V_b
| V_a_H = V_b_H
| V_a = V_b_H
| V_b = V_a_H
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__X1__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__X1__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H))) ),
file('theBenchmark.p',cls_1_0) ).
cnf(cls_1_1,axiom,
( V_a = V_b
| V_a_H = V_b_H
| V_a = V_b_H
| V_b = V_a_H
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__X1__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__X1__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H))) ),
file('theBenchmark.p',cls_1_1) ).
cnf(cls_2_0,axiom,
( V_a = V_b
| V_a_H = V_b_H
| V_a = V_b_H
| V_b = V_a_H
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__X2__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__X2__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H))) ),
file('theBenchmark.p',cls_2_0) ).
cnf(cls_2_1,axiom,
( V_a = V_b
| V_a_H = V_b_H
| V_a = V_b_H
| V_b = V_a_H
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__X2__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__X2__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P))) ),
file('theBenchmark.p',cls_2_1) ).
cnf(cls_2_2,axiom,
( V_a = V_b
| V_a_H = V_b_H
| V_a = V_b_H
| V_b = V_a_H
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__X2__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__X2__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H))) ),
file('theBenchmark.p',cls_2_2) ).
cnf(cls_2_3,axiom,
( V_a = V_b
| V_a_H = V_b_H
| V_a = V_b_H
| V_b = V_a_H
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__X2__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__X2__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P))) ),
file('theBenchmark.p',cls_2_3) ).
cnf(cls_pairwise__neutrality_0,axiom,
( V_a = V_b
| V_a_H = V_b_H
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__Xpairwise__neutrality__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__Xpairwise__neutrality__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H))) ),
file('theBenchmark.p',cls_pairwise__neutrality_0) ).
cnf(cls_pairwise__neutrality_1,axiom,
( V_a = V_b
| V_a_H = V_b_H
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__Xpairwise__neutrality__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__Xpairwise__neutrality__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P))) ),
file('theBenchmark.p',cls_pairwise__neutrality_1) ).
cnf(cls_pairwise__neutrality_2,axiom,
( V_a = V_b
| V_a_H = V_b_H
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__Xpairwise__neutrality__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__Xpairwise__neutrality__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H))) ),
file('theBenchmark.p',cls_pairwise__neutrality_2) ).
cnf(cls_pairwise__neutrality_3,axiom,
( V_a = V_b
| V_a_H = V_b_H
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__Xpairwise__neutrality__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__Xpairwise__neutrality__1(V_P,V_P_H,V_a,V_a_H,V_b,V_b_H))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a_H,V_b_H,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P))) ),
file('theBenchmark.p',cls_pairwise__neutrality_3) ).
cnf(cls_3_0,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__X3__1(V_P,V_P_H,V_a,V_b))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__X3__1(V_P,V_P_H,V_a,V_b))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H))) ),
file('theBenchmark.p',cls_3_0) ).
cnf(cls_3_1,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__X3__1(V_P,V_P_H,V_a,V_b))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__X3__1(V_P,V_P_H,V_a,V_b))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P))) ),
file('theBenchmark.p',cls_3_1) ).
cnf(cls_3_2,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__X3__1(V_P,V_P_H,V_a,V_b))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__X3__1(V_P,V_P_H,V_a,V_b))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H))) ),
file('theBenchmark.p',cls_3_2) ).
cnf(cls_3_3,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__X3__1(V_P,V_P_H,V_a,V_b))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__X3__1(V_P,V_P_H,V_a,V_b))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P))) ),
file('theBenchmark.p',cls_3_3) ).
cnf(cls_4_0,axiom,
( V_a = V_b
| V_b = V_c
| V_a = V_c
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__X4__1(V_P,V_P_H,V_a,V_b,V_c))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_c,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__X4__1(V_P,V_P_H,V_a,V_b,V_c))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_c,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H))) ),
file('theBenchmark.p',cls_4_0) ).
cnf(cls_4_1,axiom,
( V_a = V_b
| V_b = V_c
| V_a = V_c
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__X4__1(V_P,V_P_H,V_a,V_b,V_c))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_c,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__X4__1(V_P,V_P_H,V_a,V_b,V_c))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_c,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P))) ),
file('theBenchmark.p',cls_4_1) ).
cnf(cls_4_2,axiom,
( V_a = V_b
| V_b = V_c
| V_a = V_c
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__X4__1(V_P,V_P_H,V_a,V_b,V_c))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_c,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__X4__1(V_P,V_P_H,V_a,V_b,V_c))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_c,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H))) ),
file('theBenchmark.p',cls_4_2) ).
cnf(cls_4_3,axiom,
( V_a = V_b
| V_b = V_c
| V_a = V_c
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_P_H),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P,v_sko__local__X4__1(V_P,V_P_H,V_a,V_b,V_c))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_c,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_P_H,v_sko__local__X4__1(V_P,V_P_H,V_a,V_b,V_c))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_c,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P_H)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,V_P))) ),
file('theBenchmark.p',cls_4_3) ).
cnf(cls_IIA__def_0,axiom,
( ~ c_Arrow__Order__Mirabelle_OIIA(V_F)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_x),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_xa),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_x,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(V_a,V_b,V_x,V_xa))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_xa,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(V_a,V_b,V_x,V_xa))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_F,V_x)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_F,V_xa))) ),
file('theBenchmark.p',cls_IIA__def_0) ).
cnf(cls_IIA__def_1,axiom,
( ~ c_Arrow__Order__Mirabelle_OIIA(V_F)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_x),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_xa),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_x,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(V_a,V_b,V_x,V_xa))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_xa,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(V_a,V_b,V_x,V_xa))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_F,V_xa)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_F,V_x))) ),
file('theBenchmark.p',cls_IIA__def_1) ).
cnf(cls_IIA__def_2,axiom,
( ~ c_Arrow__Order__Mirabelle_OIIA(V_F)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_x),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_xa),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_x,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(V_a,V_b,V_x,V_xa))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_xa,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(V_a,V_b,V_x,V_xa))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_F,V_x)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_F,V_xa))) ),
file('theBenchmark.p',cls_IIA__def_2) ).
cnf(cls_IIA__def_3,axiom,
( ~ c_Arrow__Order__Mirabelle_OIIA(V_F)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_x),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_xa),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_x,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(V_a,V_b,V_x,V_xa))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_xa,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(V_a,V_b,V_x,V_xa))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_F,V_xa)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_F,V_x))) ),
file('theBenchmark.p',cls_IIA__def_3) ).
cnf(cls_unanimity__def_0,axiom,
( ~ c_Arrow__Order__Mirabelle_Ounanimity(V_F)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),V_x),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_x,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(V_a,V_b,V_x))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(V_F,V_x))) ),
file('theBenchmark.p',cls_unanimity__def_0) ).
cnf(cls_eq__equiv__class__iff2_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))
| ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_r,T_a) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(V_y,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_r,T_a) ),
file('theBenchmark.p',cls_eq__equiv__class__iff2_0) ).
cnf(cls_eq__equiv__class__iff2_1,axiom,
( ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_r,T_a) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(V_y,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_r,T_a) ),
file('theBenchmark.p',cls_eq__equiv__class__iff2_1) ).
cnf(cls_quotientE_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_X),c_Equiv__Relations_Oquotient(V_A,V_r,T_a)))
| V_X = c_Relation_OImage(V_r,c_Set_Oinsert(c_List_Osko__Equiv__Relations__XquotientE__1__1(V_A,V_X,V_r,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) ),
file('theBenchmark.p',cls_quotientE_0) ).
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_in__mkbot_3,axiom,
( V_y = V_z
| V_x = V_z
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_z))) ),
file('theBenchmark.p',cls_in__mkbot_3) ).
cnf(cls_in__mkbot_5,axiom,
( V_y = V_z
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_z))) ),
file('theBenchmark.p',cls_in__mkbot_5) ).
cnf(cls_SigmaD1_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Product__Type_OSigma(V_A,V_B,T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ),
file('theBenchmark.p',cls_SigmaD1_0) ).
cnf(cls_SigmaD2_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Product__Type_OSigma(V_A,V_B,T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),V_b),hAPP(V_B,V_a))) ),
file('theBenchmark.p',cls_SigmaD2_0) ).
cnf(cls_UnionE_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_Complete__Lattice_OSup__class_OSup(V_C,tc_fun(T_a,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(V_A,V_C,T_a))) ),
file('theBenchmark.p',cls_UnionE_0) ).
cnf(cls_bij__betw__restrict__eq_0,axiom,
( ~ c_Fun_Obij__betw(c_FuncSet_Orestrict(V_f,V_A,T_a,T_b),V_A,V_B,T_a,T_b)
| c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) ),
file('theBenchmark.p',cls_bij__betw__restrict__eq_0) ).
cnf(cls_bij__betw__restrict__eq_1,axiom,
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Obij__betw(c_FuncSet_Orestrict(V_f,V_A,T_a,T_b),V_A,V_B,T_a,T_b) ),
file('theBenchmark.p',cls_bij__betw__restrict__eq_1) ).
cnf(cls_inj__on__insert_2,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| hBOOL(hAPP(hAPP(c_in(T_b),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)))
| 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_Id__compose_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_Oextensional(V_A,T_a,T_b)))
| c_FuncSet_Ocompose(V_A,c_FuncSet_Orestrict(c_COMBI(T_b),V_B,T_b,T_b),V_f,T_a,T_b,T_b) = V_f ),
file('theBenchmark.p',cls_Id__compose_0) ).
cnf(cls_compose__Id_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_g),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_g),c_FuncSet_Oextensional(V_A,T_a,T_b)))
| c_FuncSet_Ocompose(V_A,V_g,c_FuncSet_Orestrict(c_COMBI(T_a),V_A,T_a,T_a),T_a,T_a,T_b) = V_g ),
file('theBenchmark.p',cls_compose__Id_0) ).
cnf(cls_Int__Collect_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Collect(V_P,T_a),tc_fun(T_a,tc_bool))))
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_Int__Collect_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_singletonE_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)))
| V_b = V_a ),
file('theBenchmark.p',cls_singletonE_0) ).
cnf(cls_InterI_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(V_A,V_C,T_a)))
| hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_Complete__Lattice_OInf__class_OInf(V_C,tc_fun(T_a,tc_bool)))) ),
file('theBenchmark.p',cls_InterI_1) ).
cnf(cls_image__constant_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| c_Set_Oimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b) ),
file('theBenchmark.p',cls_image__constant_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_insert__Diff1_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| 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_image__ident_0,axiom,
c_Set_Oimage(c_COMBI(T_a),V_Y,T_a,T_a) = V_Y,
file('theBenchmark.p',cls_image__ident_0) ).
cnf(cls_complete__lattice_OSup__UNIV_0,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a)
| hAPP(V_Sup,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = V_top ),
file('theBenchmark.p',cls_complete__lattice_OSup__UNIV_0) ).
cnf(cls_complete__lattice_OInf__UNIV_0,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a)
| hAPP(V_Inf,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = V_bot ),
file('theBenchmark.p',cls_complete__lattice_OInf__UNIV_0) ).
cnf(cls_in__mkbot_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x))),
file('theBenchmark.p',cls_in__mkbot_0) ).
cnf(cls_in__mkbot_1,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x))),
file('theBenchmark.p',cls_in__mkbot_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_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_Inf__insert_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(V_a,V_A,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_a,c_Complete__Lattice_OInf__class_OInf(V_A,T_a),T_a)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_Inf__insert_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_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_Collect__def_0,axiom,
c_Collect(V_P,T_a) = V_P,
file('theBenchmark.p',cls_Collect__def_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_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__id2_0,axiom,
c_Fun_Oinj__on(c_COMBI(T_a),V_A,T_a,T_a),
file('theBenchmark.p',cls_inj__on__id2_0) ).
cnf(cls_vimage__singleton__eq_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_aa),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))),
file('theBenchmark.p',cls_vimage__singleton__eq_1) ).
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__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_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_UNION__empty__conv_I2_J_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| hAPP(V_B,V_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_UNION__empty__conv_I2_J_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_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_complete__lattice_OSup__binary_0,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a)
| hAPP(V_Sup,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)) = hAPP(hAPP(V_sup,V_a),V_b) ),
file('theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
cnf(cls_complete__lattice_OInf__binary_0,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a)
| hAPP(V_Inf,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)) = hAPP(hAPP(V_inf,V_a),V_b) ),
file('theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
cnf(cls_Sup__empty_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) = c_Orderings_Obot__class_Obot(T_a)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_Sup__empty_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_INT__extend__simps_I4_J_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A,
file('theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(V_P,T_b,T_c,T_a),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q),
file('theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_COMBI__def_0,axiom,
hAPP(c_COMBI(T_a),V_P) = V_P,
file('theBenchmark.p',cls_COMBI__def_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_rangeI_0,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),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))),
file('theBenchmark.p',cls_rangeI_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_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_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_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_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_complete__lattice_Odual__complete__lattice_0,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a)
| c_Complete__Lattice_Ocomplete__lattice(V_Sup,V_Inf,c_COMBC(V_less__eq,T_a,T_a,tc_bool),c_COMBC(V_less,T_a,T_a,tc_bool),V_sup,V_inf,V_top,V_bot,T_a) ),
file('theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_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_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_in__mktop_4,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x)))
| V_xa = V_x
| V_xa = V_x ),
file('theBenchmark.p',cls_in__mktop_4) ).
cnf(cls_image__constant__conv_0,axiom,
c_Set_Oimage(c_COMBK(V_c,T_a,T_b),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__constant__conv_0) ).
cnf(cls_comm__monoid__add_Ononempty__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_xa))
| 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_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_UN__constant_1,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBK(V_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = V_c ),
file('theBenchmark.p',cls_UN__constant_1) ).
cnf(cls_SUP__const_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBK(V_M,T_b,T_a),T_a,T_b) = V_M
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
file('theBenchmark.p',cls_SUP__const_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,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_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_Int__insert__right_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_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_Int__insert__left_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_C))
| 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_UN__constant_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),c_COMBK(V_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_UN__constant_0) ).
cnf(cls_in__mkbot_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_z)))
| V_x = V_z
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_in__mkbot_2) ).
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_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_Inf__singleton_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_Inf__singleton_0) ).
cnf(cls_Int__Collect_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Collect(V_P,T_a),tc_fun(T_a,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ),
file('theBenchmark.p',cls_Int__Collect_0) ).
cnf(cls_complete__Lin_1,axiom,
( V_a = V_b
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b))) ),
file('theBenchmark.p',cls_complete__Lin_1) ).
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)
| ~ hBOOL(hAPP(hAPP(c_in(T_b),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))) ),
file('theBenchmark.p',cls_inj__on__insert_1) ).
cnf(cls_Union__disjoint_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_x),V_C))
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(V_C,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_Union__disjoint_0) ).
cnf(cls_insert__Diff__if_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| 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_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_Sup__UNIV_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a) = c_Orderings_Otop__class_Otop(T_a)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_Sup__UNIV_0) ).
cnf(cls_Diff__insert__absorb_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_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_bij__betw__def_0,axiom,
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ),
file('theBenchmark.p',cls_bij__betw__def_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_Inf__binary_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(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),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_Inf__binary_0) ).
cnf(cls_in__above_0,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_a,V_b))) ),
file('theBenchmark.p',cls_in__above_0) ).
cnf(cls_in__above_7,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_a,V_x)))
| V_a = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_xa = V_x
| V_xa = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_in__above_7) ).
cnf(cls_in__above_6,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_x,V_b)))
| V_x = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| V_x = V_b ),
file('theBenchmark.p',cls_in__above_6) ).
cnf(cls_in__above_3,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_a,V_b)))
| V_x = V_b
| V_y = V_b
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_in__above_3) ).
cnf(cls_in__above_2,axiom,
( V_xa = V_a
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| V_a = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_a,V_x)))
| V_xa = V_x ),
file('theBenchmark.p',cls_in__above_2) ).
cnf(cls_in__above_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| V_a = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_a,V_x))) ),
file('theBenchmark.p',cls_in__above_1) ).
cnf(cls_in__below_13,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_x,V_b)))
| V_x = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_in__below_13) ).
cnf(cls_in__below_12,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_a,V_x)))
| V_a = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_xa = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_in__below_12) ).
cnf(cls_in__below_10,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| V_x = V_a
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_a,V_b))) ),
file('theBenchmark.p',cls_in__below_10) ).
cnf(cls_in__below_8,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| V_y = V_a
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_a,V_b))) ),
file('theBenchmark.p',cls_in__below_8) ).
cnf(cls_in__below_5,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_x,V_xa)))
| V_x = V_xa
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_xa
| V_xa = V_x ),
file('theBenchmark.p',cls_in__below_5) ).
cnf(cls_in__above_14,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_a,V_b))) ),
file('theBenchmark.p',cls_in__above_14) ).
cnf(cls_in__above_11,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_xa,V_x)))
| V_xa = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_xa = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_in__above_11) ).
cnf(cls_in__above_9,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_a,V_x)))
| V_a = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_in__above_9) ).
cnf(cls_in__above_4,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| V_x = V_b
| V_y = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_a,V_b))) ),
file('theBenchmark.p',cls_in__above_4) ).
cnf(cls_in__below_0,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_a,V_b))) ),
file('theBenchmark.p',cls_in__below_0) ).
cnf(cls_in__below_7,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_x,V_b)))
| V_x = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| V_y = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_in__below_7) ).
cnf(cls_in__below_6,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_a,V_x)))
| V_a = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_xa = V_x
| V_x = V_a ),
file('theBenchmark.p',cls_in__below_6) ).
cnf(cls_in__below_3,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_a,V_b)))
| V_y = V_a
| V_x = V_a
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_in__below_3) ).
cnf(cls_in__below_2,axiom,
( V_y = V_b
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| V_x = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_x,V_b)))
| V_y = V_x ),
file('theBenchmark.p',cls_in__below_2) ).
cnf(cls_in__below_1,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| V_x = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_x,V_b))) ),
file('theBenchmark.p',cls_in__below_1) ).
cnf(cls_in__above_13,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_a,V_x)))
| V_a = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_xa = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_in__above_13) ).
cnf(cls_in__above_12,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_x,V_b)))
| V_x = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_in__above_12) ).
cnf(cls_in__above_10,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| V_y = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_a,V_b))) ),
file('theBenchmark.p',cls_in__above_10) ).
cnf(cls_in__above_8,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| V_x = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_a,V_b))) ),
file('theBenchmark.p',cls_in__above_8) ).
cnf(cls_in__above_5,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_xa,V_x)))
| V_xa = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_xa = V_x
| V_xa = V_x ),
file('theBenchmark.p',cls_in__above_5) ).
cnf(cls_in__below_14,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_a,V_b))) ),
file('theBenchmark.p',cls_in__below_14) ).
cnf(cls_in__below_11,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_x,V_xa)))
| V_x = V_xa
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_xa
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_in__below_11) ).
cnf(cls_in__below_9,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_x,V_b)))
| V_x = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_xa = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_in__below_9) ).
cnf(cls_in__below_4,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| V_y = V_a
| V_x = V_a
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_a,V_b))) ),
file('theBenchmark.p',cls_in__below_4) ).
cnf(cls_bexCI_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XbexCI__1__1(V_A,V_P,T_a))) ),
file('theBenchmark.p',cls_bexCI_1) ).
cnf(cls_Int__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)))) ),
file('theBenchmark.p',cls_Int__iff_2) ).
cnf(cls_IntI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)))) ),
file('theBenchmark.p',cls_IntI_0) ).
cnf(cls_ord_OatLeastLessThan__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i))
| ~ hBOOL(hAPP(hAPP(V_less,V_i),V_u))
| hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastLessThan(V_less__eq,V_less,V_l,V_u,T_a))) ),
file('theBenchmark.p',cls_ord_OatLeastLessThan__iff_2) ).
cnf(cls_insert__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_b,V_A,T_a))) ),
file('theBenchmark.p',cls_insert__iff_2) ).
cnf(cls_insertCI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_b,V_B,T_a))) ),
file('theBenchmark.p',cls_insertCI_0) ).
cnf(cls_restrict__apply_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| hAPP(c_FuncSet_Orestrict(V_f,V_A,T_b,T_a),V_x) = hAPP(V_f,V_x) ),
file('theBenchmark.p',cls_restrict__apply_0) ).
cnf(cls_ord_OatLeastAtMost__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_i),V_u))
| hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastAtMost(V_less__eq,V_l,V_u,T_a))) ),
file('theBenchmark.p',cls_ord_OatLeastAtMost__iff_2) ).
cnf(cls_bexCI_2,axiom,
( ~ hBOOL(hAPP(V_P,V_a))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__XbexCI__1__1(V_A,V_P,T_a)),V_A)) ),
file('theBenchmark.p',cls_bexCI_2) ).
cnf(cls_ex__in__conv_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
file('theBenchmark.p',cls_ex__in__conv_0) ).
cnf(cls_ball__empty_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_ball__empty_0) ).
cnf(cls_empty__iff_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
file('theBenchmark.p',cls_empty__iff_0) ).
cnf(cls_emptyE_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
file('theBenchmark.p',cls_emptyE_0) ).
cnf(cls_ord_OgreaterThanLessThan__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(V_less,V_l),V_i))
| ~ hBOOL(hAPP(hAPP(V_less,V_i),V_u))
| hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThanLessThan(V_less,V_l,V_u,T_a))) ),
file('theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_2) ).
cnf(cls_insertE_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_b,V_A,T_a)))
| V_a = V_b
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ),
file('theBenchmark.p',cls_insertE_0) ).
cnf(cls_compose__eq_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hAPP(c_FuncSet_Ocompose(V_A,V_g,V_f,T_a,T_c,T_b),V_x) = hAPP(V_g,hAPP(V_f,V_x)) ),
file('theBenchmark.p',cls_compose__eq_0) ).
cnf(cls_UNIV__I_0,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)))),
file('theBenchmark.p',cls_UNIV__I_0) ).
cnf(cls_DiffE_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B)) ),
file('theBenchmark.p',cls_DiffE_1) ).
cnf(cls_DiffE_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ),
file('theBenchmark.p',cls_DiffE_0) ).
cnf(cls_bexCI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__XbexCI__1__1(V_A,V_P,T_a)),V_A)) ),
file('theBenchmark.p',cls_bexCI_0) ).
cnf(cls_bexI_1,axiom,
( ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XbexI__1__1(V_A,V_P,T_a))) ),
file('theBenchmark.p',cls_bexI_1) ).
cnf(cls_bexE_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(V_P,V_x))
| hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XbexE__1__1(V_A,V_P,T_a))) ),
file('theBenchmark.p',cls_bexE_1) ).
cnf(cls_insert__iff_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,V_A,T_a))),
file('theBenchmark.p',cls_insert__iff_1) ).
cnf(cls_insertI1_0,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_a,V_B,T_a))),
file('theBenchmark.p',cls_insertI1_0) ).
cnf(cls_insertCI_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,V_B,T_a))),
file('theBenchmark.p',cls_insertCI_1) ).
cnf(cls_ball__conj__distrib_3,axiom,
( ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a)))
| ~ hBOOL(hAPP(V_Q,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xf),V_A))
| hBOOL(hAPP(V_Q,V_xf)) ),
file('theBenchmark.p',cls_ball__conj__distrib_3) ).
cnf(cls_ball__conj__distrib_2,axiom,
( ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a)))
| ~ hBOOL(hAPP(V_Q,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xg),V_A))
| hBOOL(hAPP(V_P,V_xg)) ),
file('theBenchmark.p',cls_ball__conj__distrib_2) ).
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)
| ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),c_Set_Oimage(V_f,V_A,T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ),
file('theBenchmark.p',cls_inj__image__mem__iff_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)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),c_Set_Oimage(V_f,V_A,T_a,T_b))) ),
file('theBenchmark.p',cls_inj__image__mem__iff_1) ).
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_in__mkbot_4,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x)))
| V_y = V_x
| V_x = V_y ),
file('theBenchmark.p',cls_in__mkbot_4) ).
cnf(cls_vimage__ident_0,axiom,
c_Set_Ovimage(c_COMBI(T_a),V_Y,T_a,T_a) = V_Y,
file('theBenchmark.p',cls_vimage__ident_0) ).
cnf(cls_converse__converse_0,axiom,
c_Relation_Oconverse(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = V_r,
file('theBenchmark.p',cls_converse__converse_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_restrict__apply_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| hAPP(c_FuncSet_Orestrict(V_f,V_A,T_b,T_a),V_x) = c_HOL_Oundefined(T_a) ),
file('theBenchmark.p',cls_restrict__apply_1) ).
cnf(cls_UNION__empty__conv_I1_J_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| hAPP(V_B,V_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_UNION__empty__conv_I1_J_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_bij__betw__def_2,axiom,
( c_Fun_Obij__betw(V_f,V_A,c_Set_Oimage(V_f,V_A,T_a,T_b),T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ),
file('theBenchmark.p',cls_bij__betw__def_2) ).
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_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_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_image__constant__conv_1,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| c_Set_Oimage(c_COMBK(V_c,T_a,T_b),V_A,T_b,T_a) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
file('theBenchmark.p',cls_image__constant__conv_1) ).
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_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))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ),
file('theBenchmark.p',cls_disjoint__iff__not__equal_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_image__restrict__eq_0,axiom,
c_Set_Oimage(c_FuncSet_Orestrict(V_f,V_A,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_image__restrict__eq_0) ).
cnf(cls_bij__betw__compose_0,axiom,
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ~ c_Fun_Obij__betw(V_g,V_B,V_C,T_b,T_c)
| c_Fun_Obij__betw(c_FuncSet_Ocompose(V_A,V_g,V_f,T_a,T_b,T_c),V_A,V_C,T_a,T_c) ),
file('theBenchmark.p',cls_bij__betw__compose_0) ).
cnf(cls_Pow__bottom_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Set_OPow(V_B,T_a))),
file('theBenchmark.p',cls_Pow__bottom_0) ).
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_Inf__UNIV_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a) = c_Orderings_Obot__class_Obot(T_a)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_Inf__UNIV_0) ).
cnf(cls_restrict__extensional_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(V_f,V_A,T_a,T_b)),c_FuncSet_Oextensional(V_A,T_a,T_b))),
file('theBenchmark.p',cls_restrict__extensional_0) ).
cnf(cls_extensionalityI_1,axiom,
( V_f = V_g
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_Oextensional(V_A,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_g),c_FuncSet_Oextensional(V_A,T_a,T_b)))
| hAPP(V_f,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(V_A,V_f,V_g,T_a,T_b)) != hAPP(V_g,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(V_A,V_f,V_g,T_a,T_b)) ),
file('theBenchmark.p',cls_extensionalityI_1) ).
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_in__mktop_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_z)))
| V_y = V_z
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_in__mktop_2) ).
cnf(cls_Collect__empty__eq_0,axiom,
( ~ hBOOL(hAPP(V_P,V_x))
| c_Collect(V_P,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_Collect__empty__eq_0) ).
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_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_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_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_surj__compose_0,axiom,
c_Set_Oimage(c_FuncSet_Ocompose(V_A,V_g,V_f,T_b,T_a,T_c),V_A,T_b,T_c) = c_Set_Oimage(V_g,c_Set_Oimage(V_f,V_A,T_b,T_a),T_a,T_c),
file('theBenchmark.p',cls_surj__compose_0) ).
cnf(cls_complete__lattice_OSup__insert_0,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a)
| hAPP(V_Sup,c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(V_sup,V_a),hAPP(V_Sup,V_A)) ),
file('theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
cnf(cls_complete__lattice_OInf__insert_0,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a)
| hAPP(V_Inf,c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(V_inf,V_a),hAPP(V_Inf,V_A)) ),
file('theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
cnf(cls_bex__UN_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),hAPP(V_B,V_x)))
| ~ hBOOL(hAPP(V_P,V_xa))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(V_A,V_B,V_P,T_b,T_a)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)))) ),
file('theBenchmark.p',cls_bex__UN_3) ).
cnf(cls_inj__on__restrict__eq_0,axiom,
( ~ c_Fun_Oinj__on(c_FuncSet_Orestrict(V_f,V_A,T_a,T_b),V_A,T_a,T_b)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ),
file('theBenchmark.p',cls_inj__on__restrict__eq_0) ).
cnf(cls_inj__on__restrict__eq_1,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| c_Fun_Oinj__on(c_FuncSet_Orestrict(V_f,V_A,T_a,T_b),V_A,T_a,T_b) ),
file('theBenchmark.p',cls_inj__on__restrict__eq_1) ).
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_in__mktop_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x))),
file('theBenchmark.p',cls_in__mktop_0) ).
cnf(cls_in__mktop_1,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x))),
file('theBenchmark.p',cls_in__mktop_1) ).
cnf(cls_update__accessor__congruence__foldE_0,axiom,
( hAPP(hAPP(V_upd,V_f),V_x) = hAPP(hAPP(V_upd,V_f_H),V_x)
| ~ c_Record_Oiso__tuple__update__accessor__cong__assist(V_upd,V_acc,T_a,T_aa)
| hAPP(V_f,hAPP(V_acc,V_x)) != hAPP(V_f_H,hAPP(V_acc,V_x)) ),
file('theBenchmark.p',cls_update__accessor__congruence__foldE_0) ).
cnf(cls_update__accessor__noopE_0,axiom,
( hAPP(hAPP(V_upd,V_f),V_x) = V_x
| ~ c_Record_Oiso__tuple__update__accessor__cong__assist(V_upd,V_acc,T_a,T_b)
| hAPP(V_f,hAPP(V_acc,V_x)) != hAPP(V_acc,V_x) ),
file('theBenchmark.p',cls_update__accessor__noopE_0) ).
cnf(cls_Int__insert__left_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_C))
| 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,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_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_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_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_vimage__singleton__eq_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),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)))
| hAPP(V_f,V_a) = V_b ),
file('theBenchmark.p',cls_vimage__singleton__eq_0) ).
cnf(cls_compose__extensional_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),c_FuncSet_Ocompose(V_A,V_f,V_g,T_a,T_c,T_b)),c_FuncSet_Oextensional(V_A,T_a,T_b))),
file('theBenchmark.p',cls_compose__extensional_0) ).
cnf(cls_UN__extend__simps_I1_J_0,axiom,
c_Set_Oinsert(V_a,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
cnf(cls_empty__Collect__eq_0,axiom,
( ~ hBOOL(hAPP(V_P,V_x))
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Collect(V_P,T_a) ),
file('theBenchmark.p',cls_empty__Collect__eq_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_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_Inf__empty_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) = c_Orderings_Otop__class_Otop(T_a)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_Inf__empty_0) ).
cnf(cls_converseD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Relation_Oconverse(V_r,T_b,T_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_a)),c_Pair(V_b,V_a,T_b,T_a)),V_r)) ),
file('theBenchmark.p',cls_converseD_0) ).
cnf(cls_converseI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),V_r))
| hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_a)),c_Pair(V_b,V_a,T_b,T_a)),c_Relation_Oconverse(V_r,T_a,T_b))) ),
file('theBenchmark.p',cls_converseI_0) ).
cnf(cls_converse__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_a)),c_Pair(V_b,V_a,T_b,T_a)),V_r))
| hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Relation_Oconverse(V_r,T_b,T_a))) ),
file('theBenchmark.p',cls_converse__iff_1) ).
cnf(cls_bij__betw__def_1,axiom,
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B ),
file('theBenchmark.p',cls_bij__betw__def_1) ).
cnf(cls_complete__lattice_OSup__empty_0,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a)
| hAPP(V_Sup,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_bot ),
file('theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
cnf(cls_complete__lattice_OInf__empty_0,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a)
| hAPP(V_Inf,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_top ),
file('theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
cnf(cls_UN__empty2_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('theBenchmark.p',cls_UN__empty2_0) ).
cnf(cls_insert__Diff_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_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_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_Sup__singleton_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_Sup__singleton_0) ).
cnf(cls_SigmaI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_b),hAPP(V_B,V_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Product__Type_OSigma(V_A,V_B,T_a,T_b))) ),
file('theBenchmark.p',cls_SigmaI_0) ).
cnf(cls_mem__Sigma__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_b),hAPP(V_B,V_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Product__Type_OSigma(V_A,V_B,T_a,T_b))) ),
file('theBenchmark.p',cls_mem__Sigma__iff_2) ).
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_singleton__conv_0,axiom,
c_Collect(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_a),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_singleton__conv_0) ).
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_complete__lattice_OSup__singleton_0,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a)
| hAPP(V_Sup,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) = V_a ),
file('theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
cnf(cls_complete__lattice_OInf__singleton_0,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a)
| hAPP(V_Inf,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) = V_a ),
file('theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
cnf(cls_Pair__eq_0,axiom,
( V_a = V_a_H
| c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b) ),
file('theBenchmark.p',cls_Pair__eq_0) ).
cnf(cls_Pair__eq_1,axiom,
( V_b = V_b_H
| c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b) ),
file('theBenchmark.p',cls_Pair__eq_1) ).
cnf(cls_singleton__iff_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))),
file('theBenchmark.p',cls_singleton__iff_1) ).
cnf(cls_Int__Collect_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(V_P,V_x))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Collect(V_P,T_a),tc_fun(T_a,tc_bool)))) ),
file('theBenchmark.p',cls_Int__Collect_2) ).
cnf(cls_Union__Pow__eq_0,axiom,
c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(V_A,T_a),tc_fun(T_a,tc_bool)) = V_A,
file('theBenchmark.p',cls_Union__Pow__eq_0) ).
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_inj__on__compose_0,axiom,
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| ~ c_Fun_Oinj__on(V_g,V_B,T_b,T_c)
| c_Fun_Oinj__on(c_FuncSet_Ocompose(V_A,V_g,V_f,T_a,T_b,T_c),V_A,T_a,T_c) ),
file('theBenchmark.p',cls_inj__on__compose_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_singleton__conv2_0,axiom,
c_Collect(hAPP(c_fequal(T_a),V_a),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
file('theBenchmark.p',cls_singleton__conv2_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_Collect__mem__eq_0,axiom,
c_Collect(hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_A),T_a) = V_A,
file('theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_in__mktop_3,axiom,
( V_x = V_z
| V_y = V_z
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_z))) ),
file('theBenchmark.p',cls_in__mktop_3) ).
cnf(cls_in__mktop_5,axiom,
( V_x = V_z
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_z))) ),
file('theBenchmark.p',cls_in__mktop_5) ).
cnf(cls_ballE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__XballE__1__1(V_A,V_P,T_a)),V_A))
| hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ),
file('theBenchmark.p',cls_ballE_0) ).
cnf(cls_bexCI_3,axiom,
( ~ hBOOL(hAPP(V_P,V_a))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XbexCI__1__1(V_A,V_P,T_a))) ),
file('theBenchmark.p',cls_bexCI_3) ).
cnf(cls_ord_OgreaterThanLessThan__iff_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThanLessThan(V_less,V_l,V_u,T_a)))
| hBOOL(hAPP(hAPP(V_less,V_l),V_i)) ),
file('theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_0) ).
cnf(cls_ord_OgreaterThanLessThan__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThanLessThan(V_less,V_l,V_u,T_a)))
| hBOOL(hAPP(hAPP(V_less,V_i),V_u)) ),
file('theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_1) ).
cnf(cls_IntE_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B)) ),
file('theBenchmark.p',cls_IntE_1) ).
cnf(cls_IntE_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_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
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_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)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_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)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_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,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_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,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(V_P,V_x)) ),
file('theBenchmark.p',cls_bex__empty_0) ).
cnf(cls_pred__equals__eq_0,axiom,
( V_R = V_S
| hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_R) != hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_S) ),
file('theBenchmark.p',cls_pred__equals__eq_0) ).
cnf(cls_CollectI_0,axiom,
( ~ hBOOL(hAPP(V_P,V_a))
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Collect(V_P,T_a))) ),
file('theBenchmark.p',cls_CollectI_0) ).
cnf(cls_CollectD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Collect(V_P,T_a)))
| hBOOL(hAPP(V_P,V_a)) ),
file('theBenchmark.p',cls_CollectD_0) ).
cnf(cls_ord_OatMost__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_less__eq,V_i),V_k))
| hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatMost(V_less__eq,V_k,T_a))) ),
file('theBenchmark.p',cls_ord_OatMost__iff_1) ).
cnf(cls_ord_OatMost__iff_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatMost(V_less__eq,V_k,T_a)))
| hBOOL(hAPP(hAPP(V_less__eq,V_i),V_k)) ),
file('theBenchmark.p',cls_ord_OatMost__iff_0) ).
cnf(cls_Diff__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)))) ),
file('theBenchmark.p',cls_Diff__iff_2) ).
cnf(cls_DiffI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)))) ),
file('theBenchmark.p',cls_DiffI_0) ).
cnf(cls_ball__conj__distrib_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a)),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xd),V_A))
| hBOOL(hAPP(V_Q,V_xd)) ),
file('theBenchmark.p',cls_ball__conj__distrib_1) ).
cnf(cls_ball__conj__distrib_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a)),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xe),V_A))
| hBOOL(hAPP(V_P,V_xe)) ),
file('theBenchmark.p',cls_ball__conj__distrib_0) ).
cnf(cls_ballE_1,axiom,
( ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XballE__1__1(V_A,V_P,T_a)))
| hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ),
file('theBenchmark.p',cls_ballE_1) ).
cnf(cls_insert__ident_0,axiom,
( V_A = V_B
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| 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_bexI_0,axiom,
( ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__XbexI__1__1(V_A,V_P,T_a)),V_A)) ),
file('theBenchmark.p',cls_bexI_0) ).
cnf(cls_UN__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),hAPP(V_B,V_x)))
| hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)))) ),
file('theBenchmark.p',cls_UN__iff_2) ).
cnf(cls_UN__I_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_b),hAPP(V_B,V_a)))
| hBOOL(hAPP(hAPP(c_in(T_b),V_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)))) ),
file('theBenchmark.p',cls_UN__I_0) ).
cnf(cls_ord_OgreaterThan__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_less,V_k),V_i))
| hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThan(V_less,V_k,T_a))) ),
file('theBenchmark.p',cls_ord_OgreaterThan__iff_1) ).
cnf(cls_ord_OgreaterThan__iff_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThan(V_less,V_k,T_a)))
| hBOOL(hAPP(hAPP(V_less,V_k),V_i)) ),
file('theBenchmark.p',cls_ord_OgreaterThan__iff_0) ).
cnf(cls_bex__UN_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),hAPP(V_B,V_x)))
| ~ hBOOL(hAPP(V_P,V_xa))
| hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(V_A,V_B,V_P,T_b,T_a))) ),
file('theBenchmark.p',cls_bex__UN_4) ).
cnf(cls_vimage__eq_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Ovimage(V_f,V_B,T_a,T_b))) ),
file('theBenchmark.p',cls_vimage__eq_1) ).
cnf(cls_vimageI2_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_a)),V_A))
| hBOOL(hAPP(hAPP(c_in(T_b),V_a),c_Set_Ovimage(V_f,V_A,T_b,T_a))) ),
file('theBenchmark.p',cls_vimageI2_0) ).
cnf(cls_vimageI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_a)),V_B))
| hBOOL(hAPP(hAPP(c_in(T_b),V_a),c_Set_Ovimage(V_f,V_B,T_b,T_a))) ),
file('theBenchmark.p',cls_vimageI_0) ).
cnf(cls_vimageE_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Ovimage(V_f,V_B,T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_B)) ),
file('theBenchmark.p',cls_vimageE_0) ).
cnf(cls_vimageD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Ovimage(V_f,V_A,T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_A)) ),
file('theBenchmark.p',cls_vimageD_0) ).
cnf(cls_complete__lattice_OInf__lower_0,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(V_less__eq,hAPP(V_Inf,V_A)),V_x)) ),
file('theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
cnf(cls_complete__lattice_OSup__upper_0,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(V_less__eq,V_x),hAPP(V_Sup,V_A))) ),
file('theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
cnf(cls_ord_OatLeastAtMost__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastAtMost(V_less__eq,V_l,V_u,T_a)))
| hBOOL(hAPP(hAPP(V_less__eq,V_i),V_u)) ),
file('theBenchmark.p',cls_ord_OatLeastAtMost__iff_1) ).
cnf(cls_ord_OatLeastAtMost__iff_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastAtMost(V_less__eq,V_l,V_u,T_a)))
| hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i)) ),
file('theBenchmark.p',cls_ord_OatLeastAtMost__iff_0) ).
cnf(cls_bex__Un_7,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(V_P,V_x))
| hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a))) ),
file('theBenchmark.p',cls_bex__Un_7) ).
cnf(cls_bex__Un_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_A))
| ~ hBOOL(hAPP(V_P,V_xa))
| hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a))) ),
file('theBenchmark.p',cls_bex__Un_5) ).
cnf(cls_bexE_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(V_P,V_x))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__XbexE__1__1(V_A,V_P,T_a)),V_A)) ),
file('theBenchmark.p',cls_bexE_0) ).
cnf(cls_insert__absorb_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| c_Set_Oinsert(V_a,V_A,T_a) = V_A ),
file('theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_ord_OlessThan__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_less,V_i),V_k))
| hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OlessThan(V_less,V_k,T_a))) ),
file('theBenchmark.p',cls_ord_OlessThan__iff_1) ).
cnf(cls_ord_OlessThan__iff_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OlessThan(V_less,V_k,T_a)))
| hBOOL(hAPP(hAPP(V_less,V_i),V_k)) ),
file('theBenchmark.p',cls_ord_OlessThan__iff_0) ).
cnf(cls_SUP2__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(hAPP(V_B,V_x),V_b),V_c))
| hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_fun(T_c,tc_bool))),V_b),V_c)) ),
file('theBenchmark.p',cls_SUP2__iff_2) ).
cnf(cls_SUP1__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(V_B,V_x),V_b))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),V_b)) ),
file('theBenchmark.p',cls_SUP1__iff_2) ).
cnf(cls_SUP2__I_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ hBOOL(hAPP(hAPP(hAPP(V_B,V_a),V_b),V_c))
| hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_fun(T_c,tc_bool))),V_b),V_c)) ),
file('theBenchmark.p',cls_SUP2__I_0) ).
cnf(cls_SUP1__I_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ hBOOL(hAPP(hAPP(V_B,V_a),V_b))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),V_b)) ),
file('theBenchmark.p',cls_SUP1__I_0) ).
cnf(cls_ord_OatLeastLessThan__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastLessThan(V_less__eq,V_less,V_l,V_u,T_a)))
| hBOOL(hAPP(hAPP(V_less,V_i),V_u)) ),
file('theBenchmark.p',cls_ord_OatLeastLessThan__iff_1) ).
cnf(cls_ord_OatLeastLessThan__iff_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastLessThan(V_less__eq,V_less,V_l,V_u,T_a)))
| hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i)) ),
file('theBenchmark.p',cls_ord_OatLeastLessThan__iff_0) ).
cnf(cls_rev__bexI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(V_P,V_x))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(V_A,V_P,T_a)),V_A)) ),
file('theBenchmark.p',cls_rev__bexI_0) ).
cnf(cls_rev__bexI_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(V_P,V_x))
| hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(V_A,V_P,T_a))) ),
file('theBenchmark.p',cls_rev__bexI_1) ).
cnf(cls_rev__image__eqI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),c_Set_Oimage(V_f,V_A,T_aa,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_aa),V_x),V_A)) ),
file('theBenchmark.p',cls_rev__image__eqI_0) ).
cnf(cls_image__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),c_Set_Oimage(V_f,V_A,T_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ),
file('theBenchmark.p',cls_image__iff_2) ).
cnf(cls_image__eqI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),c_Set_Oimage(V_f,V_A,T_b,T_a))) ),
file('theBenchmark.p',cls_image__eqI_0) ).
cnf(cls_imageI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),c_Set_Oimage(V_f,V_A,T_a,T_b))) ),
file('theBenchmark.p',cls_imageI_0) ).
cnf(cls_Pi__I_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_FuncSet_Osko__FuncSet__XPi__I__1__1(V_A,V_B,V_f,T_a,T_b)),V_A))
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,V_B,T_a,T_b))) ),
file('theBenchmark.p',cls_Pi__I_0) ).
cnf(cls_Pi__I_H_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(V_A,V_B,V_f,T_a,T_b)),V_A))
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,V_B,T_a,T_b))) ),
file('theBenchmark.p',cls_Pi__I_H_0) ).
cnf(cls_extensional__arb_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_Oextensional(V_A,T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hAPP(V_f,V_x) = c_HOL_Oundefined(T_b) ),
file('theBenchmark.p',cls_extensional__arb_0) ).
cnf(cls_Pi__I_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,c_FuncSet_Osko__FuncSet__XPi__I__1__1(V_A,V_B,V_f,T_a,T_b))),hAPP(V_B,c_FuncSet_Osko__FuncSet__XPi__I__1__1(V_A,V_B,V_f,T_a,T_b))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,V_B,T_a,T_b))) ),
file('theBenchmark.p',cls_Pi__I_1) ).
cnf(cls_extensionalityI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_Oextensional(V_A,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_g),c_FuncSet_Oextensional(V_A,T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_a),c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(V_A,V_f,V_g,T_a,T_b)),V_A))
| V_f = V_g ),
file('theBenchmark.p',cls_extensionalityI_0) ).
cnf(cls_Pi__I_H_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(V_A,V_B,V_f,T_a,T_b))),hAPP(V_B,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(V_A,V_B,V_f,T_a,T_b))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,V_B,T_a,T_b))) ),
file('theBenchmark.p',cls_Pi__I_H_1) ).
cnf(cls_InterI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(V_A,V_C,T_a)),V_C))
| hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_Complete__Lattice_OInf__class_OInf(V_C,tc_fun(T_a,tc_bool)))) ),
file('theBenchmark.p',cls_InterI_0) ).
cnf(cls_UnionE_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_Complete__Lattice_OSup__class_OSup(V_C,tc_fun(T_a,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(V_A,V_C,T_a)),V_C)) ),
file('theBenchmark.p',cls_UnionE_1) ).
cnf(cls_quotientE_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_X),c_Equiv__Relations_Oquotient(V_A,V_r,T_a)))
| hBOOL(hAPP(hAPP(c_in(T_a),c_List_Osko__Equiv__Relations__XquotientE__1__1(V_A,V_X,V_r,T_a)),V_A)) ),
file('theBenchmark.p',cls_quotientE_1) ).
cnf(cls_vimage__const_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A))
| c_Set_Ovimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_vimage__const_0) ).
cnf(cls_vimage__const_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A))
| c_Set_Ovimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
file('theBenchmark.p',cls_vimage__const_1) ).
cnf(cls_Pow__top_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_A),c_Set_OPow(V_A,T_a))),
file('theBenchmark.p',cls_Pow__top_0) ).
cnf(cls_restrict__in__funcset_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1(V_A,V_B,V_f,T_a,T_b)),V_A))
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(V_f,V_A,T_a,T_b)),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b))) ),
file('theBenchmark.p',cls_restrict__in__funcset_0) ).
cnf(cls_restrict__in__funcset_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1(V_A,V_B,V_f,T_a,T_b))),V_B))
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),c_FuncSet_Orestrict(V_f,V_A,T_a,T_b)),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b))) ),
file('theBenchmark.p',cls_restrict__in__funcset_1) ).
cnf(cls_compose__assoc_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_b,T_c)),V_g),c_FuncSet_OPi(V_B,c_COMBK(V_C,tc_fun(T_c,tc_bool),T_b),T_b,T_c)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_c,T_d)),V_h),c_FuncSet_OPi(V_C,c_COMBK(V_D,tc_fun(T_d,tc_bool),T_c),T_c,T_d)))
| c_FuncSet_Ocompose(V_A,V_h,c_FuncSet_Ocompose(V_A,V_g,V_f,T_a,T_b,T_c),T_a,T_c,T_d) = c_FuncSet_Ocompose(V_A,c_FuncSet_Ocompose(V_B,V_h,V_g,T_b,T_c,T_d),V_f,T_a,T_b,T_d) ),
file('theBenchmark.p',cls_compose__assoc_0) ).
cnf(cls_funcset__compose_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_b,T_c)),V_g),c_FuncSet_OPi(V_B,c_COMBK(V_C,tc_fun(T_c,tc_bool),T_b),T_b,T_c)))
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_c)),c_FuncSet_Ocompose(V_A,V_g,V_f,T_a,T_b,T_c)),c_FuncSet_OPi(V_A,c_COMBK(V_C,tc_fun(T_c,tc_bool),T_a),T_a,T_c))) ),
file('theBenchmark.p',cls_funcset__compose_0) ).
cnf(cls_funcset__id_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_a)),c_COMBI(T_a)),c_FuncSet_OPi(V_A,c_COMBK(V_A,tc_fun(T_a,tc_bool),T_a),T_a,T_a))),
file('theBenchmark.p',cls_funcset__id_0) ).
cnf(cls_bij__betw__imp__funcset_0,axiom,
( ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b)
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b))) ),
file('theBenchmark.p',cls_bij__betw__imp__funcset_0) ).
cnf(cls_lfp__const_0,axiom,
( c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(V_t,T_a,T_a),T_a) = V_t
| ~ class_Complete__Lattice_Ocomplete__lattice(T_a) ),
file('theBenchmark.p',cls_lfp__const_0) ).
cnf(cls_iso__tuple__update__accessor__cong__assist__def_0,axiom,
( ~ c_Record_Oiso__tuple__update__accessor__cong__assist(V_upd,V_acc,T_a,T_b)
| hAPP(hAPP(V_upd,c_COMBK(hAPP(V_f,hAPP(V_acc,V_va)),T_a,T_a)),V_va) = hAPP(hAPP(V_upd,V_f),V_va) ),
file('theBenchmark.p',cls_iso__tuple__update__accessor__cong__assist__def_0) ).
cnf(cls_assms_I3_J_0,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('theBenchmark.p',cls_assms_I3_J_0) ).
cnf(cls_u_0,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('theBenchmark.p',cls_u_0) ).
cnf(cls_notin__Lin__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_notin__Lin__iff_1) ).
cnf(cls_notin__Lin__iff_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_notin__Lin__iff_0) ).
cnf(cls_Lin__irrefl_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
file('theBenchmark.p',cls_Lin__irrefl_0) ).
cnf(cls_funcsetI_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(V_A,V_B,V_f,T_a,T_b))),V_B))
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b))) ),
file('theBenchmark.p',cls_funcsetI_1) ).
cnf(cls_funcsetI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(V_A,V_B,V_f,T_a,T_b)),V_A))
| hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b))) ),
file('theBenchmark.p',cls_funcsetI_0) ).
cnf(cls_Pi__mem_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,V_B,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),hAPP(V_B,V_x))) ),
file('theBenchmark.p',cls_Pi__mem_0) ).
cnf(cls_PiE_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,V_B,T_a,T_b)))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),hAPP(V_B,V_x)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ),
file('theBenchmark.p',cls_PiE_0) ).
cnf(cls_InterD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_Complete__Lattice_OInf__class_OInf(V_C,tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_X),V_C))
| hBOOL(hAPP(hAPP(c_in(T_a),V_A),V_X)) ),
file('theBenchmark.p',cls_InterD_0) ).
cnf(cls_UnionI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_X),V_C))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_A),V_X))
| hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_Complete__Lattice_OSup__class_OSup(V_C,tc_fun(T_a,tc_bool)))) ),
file('theBenchmark.p',cls_UnionI_0) ).
cnf(cls_Times__eq__cancel2_0,axiom,
( V_A = V_B
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_C))
| c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a) != c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a) ),
file('theBenchmark.p',cls_Times__eq__cancel2_0) ).
cnf(cls_complete__Lin_0,axiom,
( V_a = V_b
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b)),c_Arrow__Order__Mirabelle_OLin)) ),
file('theBenchmark.p',cls_complete__Lin_0) ).
cnf(cls_mktop__Lin_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x)),c_Arrow__Order__Mirabelle_OLin)) ),
file('theBenchmark.p',cls_mktop__Lin_0) ).
cnf(cls_mkbot__Lin_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x)),c_Arrow__Order__Mirabelle_OLin)) ),
file('theBenchmark.p',cls_mkbot__Lin_0) ).
cnf(cls_below__Lin_0,axiom,
( V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_x,V_y)),c_Arrow__Order__Mirabelle_OLin)) ),
file('theBenchmark.p',cls_below__Lin_0) ).
cnf(cls_linear__alt_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1),c_Arrow__Order__Mirabelle_OLin)),
file('theBenchmark.p',cls_linear__alt_0) ).
cnf(cls_converse__in__Lin_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) ),
file('theBenchmark.p',cls_converse__in__Lin_0) ).
cnf(cls_converse__in__Lin_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(V_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin)) ),
file('theBenchmark.p',cls_converse__in__Lin_1) ).
cnf(cls_above__Lin_0,axiom,
( V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_x,V_y)),c_Arrow__Order__Mirabelle_OLin)) ),
file('theBenchmark.p',cls_above__Lin_0) ).
cnf(cls_const__Lin__Prof_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)) ),
file('theBenchmark.p',cls_const__Lin__Prof_0) ).
cnf(cls_funcset__mem_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B)) ),
file('theBenchmark.p',cls_funcset__mem_0) ).
cnf(cls_mem__def_1,axiom,
( ~ hBOOL(hAPP(V_S,V_x))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S)) ),
file('theBenchmark.p',cls_mem__def_1) ).
cnf(cls_mem__def_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S))
| hBOOL(hAPP(V_S,V_x)) ),
file('theBenchmark.p',cls_mem__def_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P,
file('theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_CHAINED_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_CHAINED_0_01,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)),
file('theBenchmark.p',cls_conjecture_0) ).
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_Oupper__semilattice,axiom,
( ~ class_Lattices_Olattice(T_1)
| class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
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_Odistrib__lattice,axiom,
( ~ class_Lattices_Odistrib__lattice(T_1)
| class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
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__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__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
file('theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
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_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
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_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
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_OCOMBK__def_0,axiom,
hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P,
file('theBenchmark.p',cls_ATP__Linkup_OCOMBK__def_0) ).
cnf(cls_ATP__Linkup_OCOMBI__def_0,axiom,
hAPP(c_COMBI(T_a),V_P) = V_P,
file('theBenchmark.p',cls_ATP__Linkup_OCOMBI__def_0) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)),
file('theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_fequal(T_a),V_X),V_Y))
| V_X = V_Y ),
file('theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
cnf(cls_quotient__eq__iff_0_simplified,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_xa,V_y,T_a,T_a)),V_r))
| ~ c_Equiv__Relations_Oequiv(V_A,V_r,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_x),c_Equiv__Relations_Oquotient(V_A,V_r,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_x)) ),
inference(simplify_clause,[status(thm)],[cls_quotient__eq__iff_0]) ).
cnf(cls_in__mktop_4_simplified,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x)))
| V_xa = V_x ),
inference(simplify_clause,[status(thm)],[cls_in__mktop_4]) ).
cnf(cls_in__above_7_simplified,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_a,V_x)))
| V_a = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_xa = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
inference(simplify_clause,[status(thm)],[cls_in__above_7]) ).
cnf(cls_in__above_6_simplified,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_x,V_b)))
| V_x = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y ),
inference(simplify_clause,[status(thm)],[cls_in__above_6]) ).
cnf(cls_in__below_12_simplified,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_a,V_x)))
| V_a = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_xa = V_x ),
inference(simplify_clause,[status(thm)],[cls_in__below_12]) ).
cnf(cls_in__below_5_simplified,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_x,V_xa)))
| V_x = V_xa
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_xa = V_x ),
inference(simplify_clause,[status(thm)],[cls_in__below_5]) ).
cnf(cls_in__above_11_simplified,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_xa,V_x)))
| V_xa = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
inference(simplify_clause,[status(thm)],[cls_in__above_11]) ).
cnf(cls_in__above_12_simplified,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_x,V_b)))
| V_x = V_b
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| V_x = V_y ),
inference(simplify_clause,[status(thm)],[cls_in__above_12]) ).
cnf(cls_in__above_5_simplified,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Oabove(V_L,V_xa,V_x)))
| V_xa = V_x
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) ),
inference(simplify_clause,[status(thm)],[cls_in__above_5]) ).
cnf(cls_in__below_11_simplified,plain,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Obelow(V_L,V_x,V_xa)))
| V_x = V_xa
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L)) ),
inference(simplify_clause,[status(thm)],[cls_in__below_11]) ).
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_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_5,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_6,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lattices_Oupper__semilattice__class_Osup(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_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_8,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_9,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_10,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_11,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_12,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_13,axiom,
( c_Relation_OImage(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Relation_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_14,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_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_COMBB(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_COMBB(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( c_Inductive_Ocomplete__lattice__class_Olfp(Eq_x_0,Eq_x_1) = c_Inductive_Ocomplete__lattice__class_Olfp(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(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_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( c_in(Eq_x_0) = c_in(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( tc_prod(Eq_x_0,Eq_x_1) = tc_prod(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_Pair(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Pair(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_23,axiom,
( c_COMBC(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_COMBC(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_24,axiom,
( c_Complete__Lattice_OSup__class_OSup(Eq_x_0,Eq_x_1) = c_Complete__Lattice_OSup__class_OSup(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( c_Complete__Lattice_OInf__class_OInf(Eq_x_0,Eq_x_1) = c_Complete__Lattice_OInf__class_OInf(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,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_27,axiom,
( c_Set_OPow(Eq_x_0,Eq_x_1) = c_Set_OPow(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_Equiv__Relations_Oquotient(Eq_x_0,Eq_x_1,Eq_x_2) = c_Equiv__Relations_Oquotient(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_29,axiom,
( c_FuncSet_Ocompose(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_FuncSet_Ocompose(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( c_FuncSet_Orestrict(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_FuncSet_Orestrict(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_31,axiom,
( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(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_32,axiom,
( c_fequal(Eq_x_0) = c_fequal(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( c_Collect(Eq_x_0,Eq_x_1) = c_Collect(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( c_Finite__Set_Osetsum(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Finite__Set_Osetsum(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_36,axiom,
( c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(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_37,axiom,
( c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( c_COMBK(Eq_x_0,Eq_x_1,Eq_x_2) = c_COMBK(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( c_FuncSet_OPi(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_FuncSet_OPi(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_40,axiom,
( c_FuncSet_Osko__FuncSet__XrestrictI__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_FuncSet_Osko__FuncSet__XrestrictI__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_COMBI(Eq_x_0) = c_COMBI(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( v_sko__local__X1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = v_sko__local__X1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( v_sko__local__X2__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = v_sko__local__X2__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( v_sko__local__Xpairwise__neutrality__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = v_sko__local__Xpairwise__neutrality__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( v_sko__local__X3__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = v_sko__local__X3__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( v_sko__local__X4__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = v_sko__local__X4__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_47,axiom,
( v_sko__Arrow__Order__Mirabelle__XIIA__def__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = v_sko__Arrow__Order__Mirabelle__XIIA__def__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(Eq_x_0,Eq_x_1,Eq_x_2) = v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( c_List_Osko__Equiv__Relations__XquotientE__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_List_Osko__Equiv__Relations__XquotientE__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,axiom,
( c_Arrow__Order__Mirabelle_Omkbot(Eq_x_0,Eq_x_1) = c_Arrow__Order__Mirabelle_Omkbot(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_51,axiom,
( c_Product__Type_OSigma(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Product__Type_OSigma(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_52,axiom,
( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( c_FuncSet_Oextensional(Eq_x_0,Eq_x_1,Eq_x_2) = c_FuncSet_Oextensional(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_54,axiom,
( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( c_Arrow__Order__Mirabelle_Omktop(Eq_x_0,Eq_x_1) = c_Arrow__Order__Mirabelle_Omktop(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(Eq_x_0,Eq_x_1) = v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__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_57,axiom,
( c_Arrow__Order__Mirabelle_Oabove(Eq_x_0,Eq_x_1,Eq_x_2) = c_Arrow__Order__Mirabelle_Oabove(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_58,axiom,
( c_Arrow__Order__Mirabelle_Obelow(Eq_x_0,Eq_x_1,Eq_x_2) = c_Arrow__Order__Mirabelle_Obelow(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_59,axiom,
( c_ATP__Linkup_Osko__Set__XbexCI__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Set__XbexCI__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( c_SetInterval_Oord_OatLeastLessThan(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_SetInterval_Oord_OatLeastLessThan(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_61,axiom,
( c_SetInterval_Oord_OatLeastAtMost(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_SetInterval_Oord_OatLeastAtMost(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_62,axiom,
( c_SetInterval_Oord_OgreaterThanLessThan(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_SetInterval_Oord_OgreaterThanLessThan(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_63,axiom,
( c_ATP__Linkup_Osko__Set__XbexI__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Set__XbexI__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( c_ATP__Linkup_Osko__Set__XbexE__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Set__XbexE__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,axiom,
( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_66,axiom,
( c_Relation_Oconverse(Eq_x_0,Eq_x_1,Eq_x_2) = c_Relation_Oconverse(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_67,axiom,
( c_HOL_Oundefined(Eq_x_0) = c_HOL_Oundefined(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,axiom,
( c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_FuncSet_Osko__FuncSet__XextensionalityI__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_69,axiom,
( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(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_70,axiom,
( c_ATP__Linkup_Osko__Set__XballE__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Set__XballE__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( c_SetInterval_Oord_OatMost(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord_OatMost(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_72,axiom,
( c_SetInterval_Oord_OgreaterThan(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord_OgreaterThan(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_73,axiom,
( c_SetInterval_Oord_OlessThan(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord_OlessThan(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_74,axiom,
( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(Eq_x_0,Eq_x_1,Eq_x_2) = c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( c_FuncSet_Osko__FuncSet__XPi__I__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_FuncSet_Osko__FuncSet__XPi__I__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_76,axiom,
( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_FuncSet_Osko__FuncSet__XPi__I_H__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_77,axiom,
( c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__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_78,axiom,
( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_FuncSet_Osko__FuncSet__XfuncsetI__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_79,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_80,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_81,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_82,axiom,
( class_Lattices_Oupper__semilattice(Eq_y_0)
| ~ class_Lattices_Oupper__semilattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_83,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_84,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_85,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_86,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_87,axiom,
( c_Finite__Set_Ofold__graph(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ c_Finite__Set_Ofold__graph(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_88,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_89,axiom,
( class_Lattices_Odistrib__lattice(Eq_y_0)
| ~ class_Lattices_Odistrib__lattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_90,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_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_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_93,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_94,axiom,
( c_Equiv__Relations_Oequiv(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Equiv__Relations_Oequiv(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_95,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_96,axiom,
( c_Fun_Obij__betw(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ c_Fun_Obij__betw(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_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_predicates]) ).
cnf(equality_97,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_98,axiom,
( c_Arrow__Order__Mirabelle_OIIA(Eq_y_0)
| ~ c_Arrow__Order__Mirabelle_OIIA(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_99,axiom,
( c_Arrow__Order__Mirabelle_Ounanimity(Eq_y_0)
| ~ c_Arrow__Order__Mirabelle_Ounanimity(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_100,axiom,
( c_Complete__Lattice_Ocomplete__lattice(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ c_Complete__Lattice_Ocomplete__lattice(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_101,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_102,axiom,
( c_Record_Oiso__tuple__update__accessor__cong__assist(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ c_Record_Oiso__tuple__update__accessor__cong__assist(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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT080-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.38 % Computer : n005.cluster.edu
% 0.08/10.38 % Model : x86_64 x86_64
% 0.08/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.38 % Memory : 8046.5625MB
% 0.08/10.38 % OS : Linux 6.8.0-71-generic
% 0.08/10.38 % CPULimit : 300
% 0.08/10.38 % WCLimit : 300
% 0.08/10.38 % DateTime : Sat Sep 19 21:11:58 UTC 2026
% 0.08/10.38 % CPUTime :
% 72.03/82.39 % SZS status Unsatisfiable for theBenchmark
% 72.03/82.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------