TSTP Solution File: ALG349-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG349-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:07:25 EDT 2023
% Result : Unsatisfiable 26.74s 26.97s
% Output : CNFRefutation 26.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 149
% Syntax : Number of formulae : 404 ( 122 unt; 67 typ; 0 def)
% Number of atoms : 632 ( 248 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 584 ( 289 ~; 295 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 122 ( 59 >; 63 *; 0 +; 0 <<)
% Number of predicates : 32 ( 30 usr; 1 prp; 0-9 aty)
% Number of functors : 37 ( 37 usr; 8 con; 0-5 aty)
% Number of variables : 608 ( 166 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
c_Set_Ovimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_24,type,
tc_bool: $i ).
tff(decl_25,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_26,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_28,type,
c_Finite__Set_Ofold: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_29,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_30,type,
c_Complete__Lattice_Ocomplete__lattice: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_31,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_32,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_33,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
tff(decl_34,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_36,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
tff(decl_37,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_38,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_39,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_40,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_41,type,
c_in: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
hBOOL: $i > $o ).
tff(decl_43,type,
c_COMBI: $i > $i ).
tff(decl_44,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_45,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_46,type,
c_Collect: ( $i * $i ) > $i ).
tff(decl_47,type,
c_ATP__Linkup_Osko__Set__XInt__Collect__mono__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_48,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(decl_49,type,
c_Complete__Lattice_OSup__class_OSup: ( $i * $i ) > $i ).
tff(decl_50,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(decl_51,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_52,type,
c_Finite__Set_Ofold1: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(decl_54,type,
class_HOL_Oord: $i > $o ).
tff(decl_55,type,
c_Lubs_OisLub: ( $i * $i * $i * $i ) > $o ).
tff(decl_56,type,
c_Lubs_OisUb: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_58,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_59,type,
tc_RealDef_Oreal: $i ).
tff(decl_60,type,
class_RealVector_Otopological__space: $i > $o ).
tff(decl_61,type,
c_RealVector_Otopological__space__class_Oclosed: ( $i * $i ) > $o ).
tff(decl_62,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_63,type,
c_Lubs_Osetle: ( $i * $i * $i ) > $o ).
tff(decl_64,type,
class_Orderings_Obot: $i > $o ).
tff(decl_65,type,
c_RealVector_Otopological__space: ( $i * $i ) > $o ).
tff(decl_66,type,
c_RealVector_Oopen__class_Oopen: $i > $i ).
tff(decl_67,type,
c_Lubs_Oubs: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
c_Lubs_Osetge: ( $i * $i * $i ) > $o ).
tff(decl_69,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
tff(decl_70,type,
t_a: $i ).
tff(decl_71,type,
v_x: $i ).
tff(decl_72,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_73,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_74,type,
v_P: $i ).
tff(decl_75,type,
v_sko__local__Xex__1: $i > $i ).
tff(decl_76,type,
v_x____: $i ).
tff(decl_77,type,
c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1: ( $i * $i * $i ) > $i ).
tff(decl_78,type,
c_Not: $i ).
tff(decl_79,type,
c_True: $i ).
tff(decl_80,type,
c_ATP__Linkup_Osko__Set__XCollect__cong__1__1: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
v_sko__local__Xthx__1: $i > $i ).
tff(decl_82,type,
class_Orderings_Otop: $i > $o ).
tff(decl_83,type,
v_sko__local__Xassms__1__1: $i > $i ).
tff(decl_84,type,
c_Deriv_Osko__Deriv__Xlemma__reals__complete__1__1: $i > $i ).
tff(decl_85,type,
c_RComplete_Osko__RComplete__Xreals__complete__1__1: $i > $i ).
tff(decl_86,type,
v_sko__CHAINED__1: $i > $i ).
tff(decl_87,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_88,type,
c_fequal: ( $i * $i * $i ) > $o ).
cnf(cls_UNIV__def_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Collect(c_COMBK(c_True,tc_bool,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__def_0) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_vimage__Collect__eq_0,axiom,
c_Set_Ovimage(X1,c_Collect(X2,X3),X4,X3) = c_Collect(c_COMBB(X2,X1,X3,tc_bool,X4),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Collect__eq_0) ).
cnf(cls_top__fun__eq_0,axiom,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
cnf(cls_vimage__const_0,axiom,
( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__const_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_mem__def_1,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(cls_le__supE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
cnf(cls_Sup__upper_0,axiom,
( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(c_in(X2,X3,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
cnf(cls_le__iff__sup_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(cls_COMBI__def_0,axiom,
hAPP(c_COMBI(X1),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
cnf(cls_vimage__empty_0,axiom,
c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).
cnf(cls_le__infI2_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(cls_assms_I1_J_0,axiom,
hBOOL(hAPP(v_P,v_sko__local__Xassms__1__1(v_P))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_assms_I1_J_0) ).
cnf(cls_sup__commute_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
cnf(cls_thx_0,axiom,
hBOOL(c_in(v_sko__local__Xthx__1(v_P),c_Collect(v_P,tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_thx_0) ).
cnf(cls_order__eq__iff_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
cnf(cls_bot__fun__eq_0,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(cls_compl__eq__compl__iff_0,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
cnf(cls_xt1_I6_J_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(cls_le__iff__inf_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
cnf(cls_le__iff__sup_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
cnf(cls_finite_0,axiom,
( c_Finite__Set_Ofinite(X2,X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).
cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
cnf(cls_le__infE_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X3),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).
cnf(clsarity_RealDef__Oreal__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olower__semilattice) ).
cnf(cls_vimage__const_1,axiom,
( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X4,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__const_1) ).
cnf(cls_double__compl_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_sup__Sup__fold__sup_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1)) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X1),X2,X3,X1,X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__Sup__fold__sup_0) ).
cnf(cls_compl__inf__bot_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
cnf(cls_compl__sup__top_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).
cnf(cls_Sup__fold__sup_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(X2,X1) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1),X2,X1,X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__fold__sup_0) ).
cnf(cls_bot__least_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
cnf(cls_le__minus__iff_1,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
cnf(cls_compl__bot__eq_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
cnf(cls_Int__Collect_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Collect(X4,X3)),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_0) ).
cnf(cls_Collect__cong_1,axiom,
( c_Collect(X1,X2) = c_Collect(X3,X2)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__cong_1) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),c_Collect(v_P,tc_RealDef_Oreal),tc_RealDef_Oreal),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_isUb__UNIV__I_1,axiom,
( hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1),X3))
| ~ class_HOL_Oord(X1)
| ~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(X2,X3,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isUb__UNIV__I_1) ).
cnf(clsarity_RealDef__Oreal__HOL_Oord,axiom,
class_HOL_Oord(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Oord) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
cnf(cls_Int__left__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
cnf(cls_inf__sup__absorb_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
cnf(cls_image__Un_0,axiom,
c_Set_Oimage(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X2,X5)),c_Set_Oimage(X1,X4,X2,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).
cnf(cls_inf__commute_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
cnf(cls_le__infE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).
cnf(cls_inf__compl__bot_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_HOL_Ouminus__class_Ouminus(X2,X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
cnf(cls_inf__eq__top__eq1_0,axiom,
( X2 = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(cls_UNIV__I_0,axiom,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
cnf(cls_order__antisym__conv_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_sup__compl__top_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_HOL_Ouminus__class_Ouminus(X2,X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).
cnf(cls_image__iff_2,axiom,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).
cnf(cls_compl__sup_0,axiom,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__sup_0) ).
cnf(cls_sup__absorb1_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
cnf(cls_Sup__UNIV_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
cnf(cls_top__greatest_0,axiom,
( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_0) ).
cnf(cls_x_0,axiom,
hBOOL(hAPP(v_P,v_x____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_x_0) ).
cnf(clsarity_fun__Lattices_Oboolean__algebra,axiom,
( class_Lattices_Oboolean__algebra(tc_fun(X1,X2))
| ~ class_Lattices_Oboolean__algebra(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
cnf(clsarity_fun__Lattices_Olattice,axiom,
( class_Lattices_Olattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
cnf(cls_image__ident_0,axiom,
c_Set_Oimage(c_COMBI(X1),X2,X1,X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__ident_0) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
cnf(cls_inf__top__left_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
cnf(cls_sup__top__right_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
cnf(cls_inf1I_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).
cnf(cls_sup__inf__absorb_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
cnf(clsarity_RealDef__Oreal__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Oupper__semilattice) ).
cnf(clsarity_fun__Lattices_Obounded__lattice,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Obounded__lattice(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
cnf(cls_Un__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(c_0_82,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Collect(c_COMBK(c_True,tc_bool,X1),X1),
cls_UNIV__def_0 ).
cnf(c_0_83,axiom,
c_Collect(X1,X2) = X1,
cls_Collect__def_0 ).
cnf(c_0_84,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_85,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_COMBK(c_True,tc_bool,X1),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_86,axiom,
c_Set_Ovimage(X1,c_Collect(X2,X3),X4,X3) = c_Collect(c_COMBB(X2,X1,X3,tc_bool,X4),X4),
cls_vimage__Collect__eq_0 ).
cnf(c_0_87,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = c_True,
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_88,axiom,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Orderings_Otop(X1) ),
cls_top__fun__eq_0 ).
cnf(c_0_89,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_90,axiom,
( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X2)) ),
cls_vimage__const_0 ).
cnf(c_0_91,plain,
c_Set_Ovimage(X1,X2,X4,X3) = c_COMBB(X2,X1,X3,tc_bool,X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_83]),c_0_83]) ).
cnf(c_0_92,plain,
c_True = c_Orderings_Otop__class_Otop(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89])]) ).
cnf(c_0_93,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_COMBB__def_0 ).
cnf(c_0_94,plain,
( c_COMBB(X4,c_COMBK(X1,X2,X3),X2,tc_bool,X3) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X2)) ),
inference(rw,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_95,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = c_Orderings_Otop__class_Otop(tc_bool),
inference(rw,[status(thm)],[c_0_87,c_0_92]) ).
cnf(c_0_96,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(X1,X2)
| ~ hBOOL(c_in(X2,X1,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]),c_0_84]) ).
cnf(c_0_97,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X2,X1)) ),
cls_mem__def_1 ).
cnf(c_0_98,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4),X3,X1) ),
cls_le__supE_0 ).
cnf(c_0_99,axiom,
( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(c_in(X2,X3,X1)) ),
cls_Sup__upper_0 ).
cnf(c_0_100,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__sup_0 ).
cnf(c_0_101,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_102,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(X1,X2)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_103,axiom,
hAPP(c_COMBI(X1),X2) = X2,
cls_COMBI__def_0 ).
cnf(c_0_104,axiom,
c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
cls_vimage__empty_0 ).
cnf(c_0_105,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ hBOOL(c_in(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X1),X4),X2,X3)) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_106,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2) = X2
| ~ c_lessequals(X1,X2,tc_bool) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_107,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
clsarity_bool__Complete__Lattice_Ocomplete__lattice ).
cnf(c_0_108,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = X1
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_109,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_110,plain,
c_COMBB(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1,X2,tc_bool,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(rw,[status(thm)],[c_0_104,c_0_91]) ).
cnf(c_0_111,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_le__infI2_0 ).
cnf(c_0_112,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_113,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_bool),tc_bool)
| ~ hBOOL(c_in(X3,X2,tc_bool))
| ~ c_lessequals(X1,X3,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_101]),c_0_107])]) ).
cnf(c_0_114,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = c_in(X1,X2,X3)
| ~ hBOOL(hAPP(X2,X1)) ),
inference(spm,[status(thm)],[c_0_108,c_0_97]) ).
cnf(c_0_115,plain,
hBOOL(c_Orderings_Otop__class_Otop(tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_88]),c_0_89])]) ).
cnf(c_0_116,axiom,
hBOOL(hAPP(v_P,v_sko__local__Xassms__1__1(v_P))),
cls_assms_I1_J_0 ).
cnf(c_0_117,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__commute_0 ).
cnf(c_0_118,axiom,
hBOOL(c_in(v_sko__local__Xthx__1(v_P),c_Collect(v_P,tc_RealDef_Oreal),tc_RealDef_Oreal)),
cls_thx_0 ).
cnf(c_0_119,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
cls_order__eq__iff_0 ).
cnf(c_0_120,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Oorder ).
cnf(c_0_121,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__fun__eq_0 ).
cnf(c_0_122,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),hAPP(X4,X2)),
inference(spm,[status(thm)],[c_0_93,c_0_110]) ).
cnf(c_0_123,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_124,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
cls_compl__eq__compl__iff_0 ).
cnf(c_0_125,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_126,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_xt1_I6_J_0 ).
cnf(c_0_127,plain,
( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2),X3,tc_bool)
| ~ c_lessequals(X2,X3,tc_bool) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_128,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_129,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__inf_0 ).
cnf(c_0_130,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_bool),tc_bool)
| ~ hBOOL(hAPP(X2,X3))
| ~ c_lessequals(X1,X3,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115])]) ).
cnf(c_0_131,plain,
hAPP(v_P,v_sko__local__Xassms__1__1(v_P)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_102,c_0_116]) ).
cnf(c_0_132,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != X3 ),
cls_le__iff__sup_1 ).
cnf(c_0_133,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X2),X1),
inference(spm,[status(thm)],[c_0_117,c_0_101]) ).
cnf(c_0_134,axiom,
( c_Finite__Set_Ofinite(X2,X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
cls_finite_0 ).
cnf(c_0_135,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
clsarity_bool__Finite__Set_Ofinite_Ofinite ).
cnf(c_0_136,plain,
hBOOL(c_in(v_sko__local__Xthx__1(v_P),v_P,tc_RealDef_Oreal)),
inference(rw,[status(thm)],[c_0_118,c_0_83]) ).
cnf(c_0_137,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X3),X1) ),
cls_le__infE_1 ).
cnf(c_0_138,plain,
c_lessequals(X1,X1,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_139,axiom,
class_Lattices_Olower__semilattice(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Lattices_Olower__semilattice ).
cnf(c_0_140,axiom,
( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X4,X2)) ),
cls_vimage__const_1 ).
cnf(c_0_141,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),hAPP(X2,v_x)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123])]) ).
cnf(c_0_142,plain,
( X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,tc_bool) != c_HOL_Ouminus__class_Ouminus(X2,tc_bool) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_143,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_double__compl_0 ).
cnf(c_0_144,plain,
( c_lessequals(X1,X2,tc_bool)
| ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X3),X4),tc_bool)
| ~ c_lessequals(X4,X2,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128])]) ).
cnf(c_0_145,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2) = X1
| ~ c_lessequals(X1,X2,tc_bool) ),
inference(spm,[status(thm)],[c_0_129,c_0_112]) ).
cnf(c_0_146,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool),tc_bool)
| ~ c_lessequals(X1,v_sko__local__Xassms__1__1(v_P),tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_115])]) ).
cnf(c_0_147,plain,
c_lessequals(X1,X1,tc_bool),
inference(spm,[status(thm)],[c_0_119,c_0_128]) ).
cnf(c_0_148,plain,
( c_lessequals(X1,X2,tc_bool)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X2),X1) != X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_101])]) ).
cnf(c_0_149,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1)) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X1),X2,X3,X1,X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_sup__Sup__fold__sup_0 ).
cnf(c_0_150,plain,
c_Finite__Set_Ofinite(X1,tc_bool),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_151,plain,
hAPP(v_P,v_sko__local__Xthx__1(v_P)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_96,c_0_136]) ).
cnf(c_0_152,plain,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_RealDef_Oreal),X1),X2),X2,tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139])]) ).
cnf(c_0_153,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__inf__bot_0 ).
cnf(c_0_154,plain,
( c_COMBB(X4,c_COMBK(X1,X2,X3),X2,tc_bool,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X4,X2)) ),
inference(rw,[status(thm)],[c_0_140,c_0_91]) ).
cnf(c_0_155,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_141,c_0_84]) ).
cnf(c_0_156,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__sup__top_0 ).
cnf(c_0_157,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_bool),tc_bool) = X1,
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_125])])]) ).
cnf(c_0_158,plain,
( c_lessequals(X1,X2,tc_bool)
| ~ c_lessequals(X1,X3,tc_bool)
| ~ c_lessequals(X4,X2,tc_bool)
| ~ c_lessequals(X3,X4,tc_bool) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_159,plain,
c_lessequals(v_sko__local__Xassms__1__1(v_P),c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool),tc_bool),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_160,plain,
( c_lessequals(c_Complete__Lattice_OSup__class_OSup(X1,tc_bool),X2,tc_bool)
| c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X2,X1,tc_bool,tc_bool) != X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_107]),c_0_150])]) ).
cnf(c_0_161,axiom,
( c_Complete__Lattice_OSup__class_OSup(X2,X1) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1),X2,X1,X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_Sup__fold__sup_0 ).
cnf(c_0_162,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__least_0 ).
cnf(c_0_163,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool),tc_bool)
| ~ c_lessequals(X1,v_sko__local__Xthx__1(v_P),tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_151]),c_0_115])]) ).
cnf(c_0_164,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_le__minus__iff_1 ).
cnf(c_0_165,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ class_Lattices_Oboolean__algebra(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_166,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add ).
cnf(c_0_167,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(X1,X2)
| hBOOL(c_in(X2,X1,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_154]),c_0_84]),c_0_155]) ).
cnf(c_0_168,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),c_HOL_Ouminus__class_Ouminus(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_125])]) ).
cnf(c_0_169,plain,
( c_lessequals(v_sko__local__Xassms__1__1(v_P),X1,tc_bool)
| ~ c_lessequals(c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool),X2,tc_bool)
| ~ c_lessequals(X2,X1,tc_bool) ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_170,plain,
( c_lessequals(c_Complete__Lattice_OSup__class_OSup(X1,tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_Complete__Lattice_OSup__class_OSup(X1,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_107]),c_0_150])]) ).
cnf(c_0_171,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool),
inference(spm,[status(thm)],[c_0_162,c_0_123]) ).
cnf(c_0_172,plain,
c_lessequals(v_sko__local__Xthx__1(v_P),c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool),tc_bool),
inference(spm,[status(thm)],[c_0_163,c_0_147]) ).
cnf(c_0_173,plain,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Lattices_Oboolean__algebra(tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_166])]) ).
cnf(c_0_174,axiom,
( c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(X1),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__bot__eq_0 ).
cnf(c_0_175,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(X1,X2)
| c_Orderings_Otop__class_Otop(tc_bool) = hAPP(X1,X2) ),
inference(spm,[status(thm)],[c_0_96,c_0_167]) ).
cnf(c_0_176,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_Collect(X4,X3)),X3)) ),
cls_Int__Collect_0 ).
cnf(c_0_177,axiom,
( c_Collect(X1,X2) = c_Collect(X3,X2)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2))) ),
cls_Collect__cong_1 ).
cnf(c_0_178,plain,
( c_HOL_Ouminus__class_Ouminus(X1,tc_bool) = c_Orderings_Otop__class_Otop(tc_bool)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_bool),tc_bool) ),
inference(spm,[status(thm)],[c_0_168,c_0_106]) ).
cnf(c_0_179,plain,
( c_lessequals(v_sko__local__Xassms__1__1(v_P),X1,tc_bool)
| c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_171])]) ).
cnf(c_0_180,plain,
( c_lessequals(v_sko__local__Xthx__1(v_P),X1,tc_bool)
| ~ c_lessequals(c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool),X2,tc_bool)
| ~ c_lessequals(X2,X1,tc_bool) ),
inference(spm,[status(thm)],[c_0_158,c_0_172]) ).
cnf(c_0_181,negated_conjecture,
~ hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),c_Collect(v_P,tc_RealDef_Oreal),tc_RealDef_Oreal),X1)),
cls_conjecture_0 ).
cnf(c_0_182,axiom,
( hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1),X3))
| ~ class_HOL_Oord(X1)
| ~ c_lessequals(c_SEQ_Osko__SEQ__XisUb__UNIV__I__1__1(X2,X3,X1),X3,X1) ),
cls_isUb__UNIV__I_1 ).
cnf(c_0_183,plain,
( c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Lattices_Oboolean__algebra(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_184,axiom,
class_HOL_Oord(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__HOL_Oord ).
cnf(c_0_185,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| c_Orderings_Otop__class_Otop(tc_bool) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_175]),c_0_103]) ).
cnf(c_0_186,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_disjoint__iff__not__equal_0 ).
cnf(c_0_187,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),
cls_Int__left__absorb_0 ).
cnf(c_0_188,plain,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3)) ),
inference(rw,[status(thm)],[c_0_176,c_0_83]) ).
cnf(c_0_189,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__absorb_0 ).
cnf(c_0_190,axiom,
c_Set_Oimage(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X2,X5)),c_Set_Oimage(X1,X4,X2,X5)),
cls_image__Un_0 ).
cnf(c_0_191,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__commute_0 ).
cnf(c_0_192,plain,
( X1 = X3
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,X3,X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_177,c_0_83]),c_0_83]) ).
cnf(c_0_193,plain,
( c_HOL_Ouminus__class_Ouminus(v_sko__local__Xassms__1__1(v_P),tc_bool) = c_Orderings_Otop__class_Otop(tc_bool)
| c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_194,plain,
( c_lessequals(v_sko__local__Xthx__1(v_P),X1,tc_bool)
| c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_170]),c_0_171])]) ).
cnf(c_0_195,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1) ),
cls_le__infE_0 ).
cnf(c_0_196,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_HOL_Ouminus__class_Ouminus(X2,X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_inf__compl__bot_0 ).
cnf(c_0_197,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| c_HOL_Ouminus__class_Ouminus(X1,tc_bool) != c_Orderings_Otop__class_Otop(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_174]),c_0_125])]) ).
cnf(c_0_198,negated_conjecture,
~ hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),v_P,tc_RealDef_Oreal),X1)),
inference(rw,[status(thm)],[c_0_181,c_0_83]) ).
cnf(c_0_199,plain,
( hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),X1,tc_RealDef_Oreal),c_Orderings_Otop__class_Otop(tc_RealDef_Oreal)))
| ~ class_Lattices_Oboolean__algebra(tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_183]),c_0_184])]) ).
cnf(c_0_200,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_115,c_0_185]) ).
cnf(c_0_201,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(c_in(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_188]) ).
cnf(c_0_202,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),c_Set_Oimage(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X5),X4,X1)) = c_Set_Oimage(X2,X3,X4,X1)
| ~ class_Lattices_Olattice(tc_fun(X1,tc_bool)) ),
inference(spm,[status(thm)],[c_0_189,c_0_190]) ).
cnf(c_0_203,axiom,
( X2 = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != c_Orderings_Otop__class_Otop(X1) ),
cls_inf__eq__top__eq1_0 ).
cnf(c_0_204,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X2),X1),
inference(spm,[status(thm)],[c_0_191,c_0_112]) ).
cnf(c_0_205,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_206,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_95]),c_0_115])]) ).
cnf(c_0_207,axiom,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)),
cls_UNIV__I_0 ).
cnf(c_0_208,plain,
( v_sko__local__Xassms__1__1(v_P) = X1
| c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool)
| c_HOL_Ouminus__class_Ouminus(X1,tc_bool) != c_Orderings_Otop__class_Otop(tc_bool) ),
inference(spm,[status(thm)],[c_0_142,c_0_193]) ).
cnf(c_0_209,plain,
( c_HOL_Ouminus__class_Ouminus(v_sko__local__Xthx__1(v_P),tc_bool) = c_Orderings_Otop__class_Otop(tc_bool)
| c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_178,c_0_194]) ).
cnf(c_0_210,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_order__antisym__conv_0 ).
cnf(c_0_211,plain,
( c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3)
| ~ class_Lattices_Oboolean__algebra(X3)
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(X3),X3) ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_212,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_HOL_Ouminus__class_Ouminus(X2,X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_sup__compl__top_0 ).
cnf(c_0_213,plain,
c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = c_Orderings_Obot__class_Obot(tc_bool),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_143]),c_0_125])])]) ).
cnf(c_0_214,negated_conjecture,
~ class_Lattices_Oboolean__algebra(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_198,c_0_199]) ).
cnf(c_0_215,plain,
( X1 = X2
| hBOOL(X1)
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_200,c_0_200]) ).
cnf(c_0_216,plain,
( c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ class_Lattices_Olattice(tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4)) ),
inference(spm,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_217,axiom,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
cls_image__iff_2 ).
cnf(c_0_218,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_bool)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X2),X1) != c_Orderings_Otop__class_Otop(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_205])]) ).
cnf(c_0_219,axiom,
( c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_HOL_Ouminus__class_Ouminus(X2,X1)),c_HOL_Ouminus__class_Ouminus(X3,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__sup_0 ).
cnf(c_0_220,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_sup__absorb1_0 ).
cnf(c_0_221,axiom,
( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
cls_Sup__UNIV_0 ).
cnf(c_0_222,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_95]),c_0_115])]) ).
cnf(c_0_223,plain,
c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_108,c_0_207]) ).
cnf(c_0_224,plain,
c_in(v_sko__local__Xthx__1(v_P),v_P,tc_RealDef_Oreal) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_108,c_0_136]) ).
cnf(c_0_225,plain,
( v_sko__local__Xthx__1(v_P) = v_sko__local__Xassms__1__1(v_P)
| c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_208,c_0_209]) ).
cnf(c_0_226,plain,
( v_sko__local__Xassms__1__1(v_P) = c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool)
| ~ c_lessequals(c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool),v_sko__local__Xassms__1__1(v_P),tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_159]),c_0_128])]) ).
cnf(c_0_227,plain,
( c_lessequals(c_Complete__Lattice_OSup__class_OSup(X1,tc_bool),X2,tc_bool)
| c_Complete__Lattice_OSup__class_OSup(X1,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_170]),c_0_112]),c_0_125])]) ).
cnf(c_0_228,axiom,
( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) ),
cls_top__greatest_0 ).
cnf(c_0_229,axiom,
hBOOL(hAPP(v_P,v_x____)),
cls_x_0 ).
cnf(c_0_230,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_125])]) ).
cnf(c_0_231,negated_conjecture,
( hBOOL(tc_RealDef_Oreal)
| hBOOL(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(spm,[status(thm)],[c_0_214,c_0_215]) ).
cnf(c_0_232,axiom,
( class_Lattices_Oboolean__algebra(tc_fun(X1,X2))
| ~ class_Lattices_Oboolean__algebra(X2) ),
clsarity_fun__Lattices_Oboolean__algebra ).
cnf(c_0_233,plain,
( c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ class_Lattices_Olattice(tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X5,X2,X3)) ),
inference(spm,[status(thm)],[c_0_216,c_0_217]) ).
cnf(c_0_234,axiom,
( class_Lattices_Olattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
clsarity_fun__Lattices_Olattice ).
cnf(c_0_235,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_236,plain,
( c_HOL_Ouminus__class_Ouminus(X1,tc_bool) = c_Orderings_Otop__class_Otop(tc_bool)
| c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X2),X1),tc_bool) != c_Orderings_Otop__class_Otop(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_219]),c_0_125])]) ).
cnf(c_0_237,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2) = X1
| ~ c_lessequals(X2,X1,tc_bool) ),
inference(spm,[status(thm)],[c_0_220,c_0_101]) ).
cnf(c_0_238,plain,
( c_Complete__Lattice_OSup__class_OSup(X1,X2) = X3
| ~ class_Orderings_Oorder(X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(c_in(X3,X1,X2))
| ~ c_lessequals(c_Complete__Lattice_OSup__class_OSup(X1,X2),X3,X2) ),
inference(spm,[status(thm)],[c_0_210,c_0_99]) ).
cnf(c_0_239,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = c_Orderings_Otop__class_Otop(X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(spm,[status(thm)],[c_0_221,c_0_222]) ).
cnf(c_0_240,plain,
c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_223,c_0_222]) ).
cnf(c_0_241,plain,
( c_in(v_sko__local__Xassms__1__1(v_P),v_P,tc_RealDef_Oreal) = c_Orderings_Otop__class_Otop(tc_bool)
| c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_224,c_0_225]) ).
cnf(c_0_242,plain,
( v_sko__local__Xassms__1__1(v_P) = c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool)
| c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_243,plain,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_bool),tc_bool),
inference(spm,[status(thm)],[c_0_228,c_0_89]) ).
cnf(c_0_244,plain,
hAPP(v_P,v_x____) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_102,c_0_229]) ).
cnf(c_0_245,plain,
( c_lessequals(X1,X2,tc_bool)
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_171]),c_0_128])]) ).
cnf(c_0_246,plain,
( c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| c_Orderings_Otop__class_Otop(tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_230]),c_0_101])]) ).
cnf(c_0_247,negated_conjecture,
( hBOOL(tc_fun(X1,X2))
| hBOOL(tc_RealDef_Oreal)
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(spm,[status(thm)],[c_0_231,c_0_232]) ).
cnf(c_0_248,plain,
( c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X5,X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_234]),c_0_235])]) ).
cnf(c_0_249,plain,
( c_HOL_Ouminus__class_Ouminus(X1,tc_bool) = c_Orderings_Otop__class_Otop(tc_bool)
| c_HOL_Ouminus__class_Ouminus(X2,tc_bool) != c_Orderings_Otop__class_Otop(tc_bool)
| ~ c_lessequals(X1,X2,tc_bool) ),
inference(spm,[status(thm)],[c_0_236,c_0_237]) ).
cnf(c_0_250,plain,
( c_Orderings_Otop__class_Otop(X1) = X2
| ~ class_Orderings_Oorder(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ c_lessequals(c_Orderings_Otop__class_Otop(X1),X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_239]),c_0_240]),c_0_115])]) ).
cnf(c_0_251,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,X1,X3)) ),
cls_mem__def_0 ).
cnf(c_0_252,plain,
( c_in(c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool),v_P,tc_RealDef_Oreal) = c_Orderings_Otop__class_Otop(tc_bool)
| c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_241,c_0_242]) ).
cnf(c_0_253,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = X1
| ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),X1,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_243]),c_0_128])]) ).
cnf(c_0_254,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool),tc_bool)
| ~ c_lessequals(X1,v_x____,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_244]),c_0_115])]) ).
cnf(c_0_255,plain,
( c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),X1,tc_bool)
| c_Orderings_Otop__class_Otop(tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_245,c_0_246]) ).
cnf(c_0_256,negated_conjecture,
( hBOOL(tc_fun(X1,tc_bool))
| hBOOL(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_247,c_0_125]) ).
cnf(c_0_257,plain,
( c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X2,X5)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_114]),c_0_115])]) ).
cnf(c_0_258,plain,
( c_HOL_Ouminus__class_Ouminus(v_sko__local__Xassms__1__1(v_P),tc_bool) = c_Orderings_Otop__class_Otop(tc_bool)
| c_HOL_Ouminus__class_Ouminus(c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool),tc_bool) != c_Orderings_Otop__class_Otop(tc_bool) ),
inference(spm,[status(thm)],[c_0_249,c_0_159]) ).
cnf(c_0_259,plain,
( c_Complete__Lattice_OSup__class_OSup(X1,X2) = c_Orderings_Otop__class_Otop(X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(X2),X1,X2)) ),
inference(spm,[status(thm)],[c_0_250,c_0_99]) ).
cnf(c_0_260,plain,
( hBOOL(hAPP(v_P,c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool)))
| c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_252]),c_0_115])]) ).
cnf(c_0_261,plain,
( c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool) = c_Orderings_Otop__class_Otop(tc_bool)
| ~ c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x____,tc_bool) ),
inference(spm,[status(thm)],[c_0_253,c_0_254]) ).
cnf(c_0_262,plain,
( c_lessequals(X1,X2,tc_bool)
| c_Orderings_Otop__class_Otop(tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_255]),c_0_128]),c_0_243])]) ).
cnf(c_0_263,negated_conjecture,
( tc_RealDef_Oreal = c_Orderings_Otop__class_Otop(tc_bool)
| hBOOL(tc_fun(X1,tc_bool)) ),
inference(spm,[status(thm)],[c_0_108,c_0_256]) ).
cnf(c_0_264,negated_conjecture,
( tc_RealDef_Oreal = c_Orderings_Obot__class_Obot(tc_bool)
| ~ class_Lattices_Oboolean__algebra(c_Orderings_Otop__class_Otop(tc_bool)) ),
inference(spm,[status(thm)],[c_0_214,c_0_185]) ).
cnf(c_0_265,plain,
c_Set_Oimage(X1,v_P,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_131]),c_0_115])]) ).
cnf(c_0_266,axiom,
c_Set_Oimage(c_COMBI(X1),X2,X1,X1) = X2,
cls_image__ident_0 ).
cnf(c_0_267,plain,
( v_sko__local__Xassms__1__1(v_P) = X1
| c_HOL_Ouminus__class_Ouminus(c_Complete__Lattice_OSup__class_OSup(v_P,tc_bool),tc_bool) != c_Orderings_Otop__class_Otop(tc_bool)
| c_HOL_Ouminus__class_Ouminus(X1,tc_bool) != c_Orderings_Otop__class_Otop(tc_bool) ),
inference(spm,[status(thm)],[c_0_142,c_0_258]) ).
cnf(c_0_268,plain,
( c_Complete__Lattice_OSup__class_OSup(X1,X2) = c_Orderings_Otop__class_Otop(X2)
| ~ class_Orderings_Oorder(X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ hBOOL(hAPP(X1,c_Orderings_Otop__class_Otop(X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_114]),c_0_115])]) ).
cnf(c_0_269,plain,
( hBOOL(hAPP(v_P,c_Orderings_Otop__class_Otop(tc_bool)))
| c_Orderings_Otop__class_Otop(tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_261]),c_0_262]) ).
cnf(c_0_270,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_bool)
| c_Orderings_Otop__class_Otop(tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_255]),c_0_128]),c_0_243])]) ).
cnf(c_0_271,negated_conjecture,
( c_Orderings_Otop__class_Otop(tc_bool) = tc_fun(X1,tc_bool)
| tc_RealDef_Oreal = c_Orderings_Otop__class_Otop(tc_bool) ),
inference(spm,[status(thm)],[c_0_108,c_0_263]) ).
cnf(c_0_272,negated_conjecture,
( tc_RealDef_Oreal = c_Orderings_Obot__class_Obot(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = X1
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(spm,[status(thm)],[c_0_264,c_0_185]) ).
cnf(c_0_273,plain,
v_P != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_265,c_0_266]) ).
cnf(c_0_274,plain,
( v_sko__local__Xassms__1__1(v_P) = X1
| c_Orderings_Otop__class_Otop(tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_267,c_0_268]),c_0_213]),c_0_128]),c_0_107])]),c_0_269]),c_0_270]) ).
cnf(c_0_275,negated_conjecture,
( tc_RealDef_Oreal = c_Orderings_Otop__class_Otop(tc_bool)
| tc_fun(X1,tc_bool) != tc_RealDef_Oreal ),
inference(ef,[status(thm)],[c_0_271]) ).
cnf(c_0_276,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_bool) = tc_bool
| tc_RealDef_Oreal = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_272,c_0_125]) ).
cnf(c_0_277,plain,
c_Orderings_Otop__class_Otop(tc_bool) != c_Orderings_Obot__class_Obot(tc_bool),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_274]),c_0_274]) ).
cnf(c_0_278,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_279,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_bool) = tc_bool
| tc_fun(X1,tc_bool) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_276]),c_0_277]) ).
cnf(c_0_280,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_278,c_0_121]),c_0_123])]) ).
cnf(c_0_281,negated_conjecture,
( tc_fun(X1,tc_bool) = tc_bool
| hBOOL(tc_fun(X1,tc_bool)) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_215]),c_0_280])]) ).
cnf(c_0_282,negated_conjecture,
( c_Orderings_Otop__class_Otop(tc_bool) = tc_fun(X1,tc_bool)
| tc_fun(X1,tc_bool) = tc_bool ),
inference(spm,[status(thm)],[c_0_108,c_0_281]) ).
cnf(c_0_283,plain,
( c_Set_Oimage(X1,c_COMBI(X2),X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ hBOOL(X5) ),
inference(spm,[status(thm)],[c_0_257,c_0_103]) ).
cnf(c_0_284,negated_conjecture,
( tc_fun(X1,tc_bool) = tc_bool
| c_Orderings_Otop__class_Otop(tc_bool) != tc_bool ),
inference(ef,[status(thm)],[c_0_282]) ).
cnf(c_0_285,plain,
( c_COMBI(X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_283,c_0_266]) ).
cnf(c_0_286,negated_conjecture,
( tc_fun(X1,tc_bool) = tc_bool
| c_Orderings_Obot__class_Obot(tc_bool) = tc_bool ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_284,c_0_185])]) ).
cnf(c_0_287,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_bool) = tc_bool
| c_COMBI(X1) != c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_285,c_0_286]) ).
cnf(c_0_288,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_bool) = tc_bool
| v_P != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_273,c_0_286]) ).
cnf(c_0_289,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_bool) = tc_bool
| hBOOL(c_COMBI(X1))
| ~ hBOOL(X2) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_287,c_0_215])]),c_0_280]) ).
cnf(c_0_290,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_bool) = tc_bool
| hBOOL(v_P) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_288,c_0_215])]),c_0_280]) ).
cnf(c_0_291,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_bool) = tc_bool
| hBOOL(c_COMBI(X1)) ),
inference(spm,[status(thm)],[c_0_289,c_0_290]) ).
cnf(c_0_292,negated_conjecture,
( c_COMBI(X1) = c_Orderings_Otop__class_Otop(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = tc_bool ),
inference(spm,[status(thm)],[c_0_108,c_0_291]) ).
cnf(c_0_293,negated_conjecture,
( hAPP(c_Orderings_Otop__class_Otop(tc_bool),X1) = c_Orderings_Otop__class_Otop(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = tc_bool ),
inference(spm,[status(thm)],[c_0_95,c_0_286]) ).
cnf(c_0_294,negated_conjecture,
( hAPP(c_Orderings_Otop__class_Otop(tc_bool),X1) = X1
| c_Orderings_Obot__class_Obot(tc_bool) = tc_bool ),
inference(spm,[status(thm)],[c_0_103,c_0_292]) ).
cnf(c_0_295,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_bool) = tc_bool
| X1 = c_Orderings_Otop__class_Otop(tc_bool) ),
inference(spm,[status(thm)],[c_0_293,c_0_294]) ).
cnf(c_0_296,negated_conjecture,
( hBOOL(tc_bool)
| hBOOL(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_231,c_0_125]) ).
cnf(c_0_297,negated_conjecture,
c_Orderings_Obot__class_Obot(tc_bool) = tc_bool,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_276,c_0_295]),c_0_277]) ).
cnf(c_0_298,negated_conjecture,
( tc_RealDef_Oreal = c_Orderings_Otop__class_Otop(tc_bool)
| hBOOL(tc_bool) ),
inference(spm,[status(thm)],[c_0_108,c_0_296]) ).
cnf(c_0_299,plain,
~ hBOOL(tc_bool),
inference(rw,[status(thm)],[c_0_280,c_0_297]) ).
cnf(c_0_300,negated_conjecture,
tc_RealDef_Oreal = c_Orderings_Otop__class_Otop(tc_bool),
inference(sr,[status(thm)],[c_0_298,c_0_299]) ).
cnf(c_0_301,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = X1
| tc_bool = X1 ),
inference(rw,[status(thm)],[c_0_185,c_0_297]) ).
cnf(c_0_302,negated_conjecture,
~ class_Lattices_Oboolean__algebra(c_Orderings_Otop__class_Otop(tc_bool)),
inference(rw,[status(thm)],[c_0_214,c_0_300]) ).
cnf(c_0_303,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__top__left_0 ).
cnf(c_0_304,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__right_0 ).
cnf(c_0_305,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X2,X4)) ),
cls_inf1I_0 ).
cnf(c_0_306,plain,
( tc_fun(X1,X2) = tc_bool
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_301]),c_0_302]) ).
cnf(c_0_307,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_sup__inf__absorb_0 ).
cnf(c_0_308,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X1) = X1,
inference(spm,[status(thm)],[c_0_303,c_0_205]) ).
cnf(c_0_309,plain,
( c_lessequals(X1,X2,X3)
| ~ class_Lattices_Obounded__lattice(X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Orderings_Otop__class_Otop(X3),X2,X3) ),
inference(spm,[status(thm)],[c_0_98,c_0_304]) ).
cnf(c_0_310,axiom,
class_Lattices_Oupper__semilattice(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Lattices_Oupper__semilattice ).
cnf(c_0_311,plain,
( ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,tc_bool)),X3))
| ~ hBOOL(hAPP(X1,X3))
| ~ class_Lattices_Oboolean__algebra(tc_fun(X2,tc_bool)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_305,c_0_196]),c_0_278]) ).
cnf(c_0_312,plain,
tc_fun(X1,tc_bool) = tc_bool,
inference(spm,[status(thm)],[c_0_306,c_0_125]) ).
cnf(c_0_313,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X1) = c_Orderings_Otop__class_Otop(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_307,c_0_308]),c_0_235])]) ).
cnf(c_0_314,plain,
( c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Lattices_Obounded__lattice(tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_309,c_0_138]),c_0_310])]) ).
cnf(c_0_315,plain,
( ~ hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(X1,tc_bool),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_311,c_0_312]),c_0_312]),c_0_125])]) ).
cnf(c_0_316,plain,
( c_HOL_Ouminus__class_Ouminus(X1,tc_bool) = c_Orderings_Otop__class_Otop(tc_bool)
| hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_200]),c_0_125])]) ).
cnf(c_0_317,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_bool),X1) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_95,c_0_312]) ).
cnf(c_0_318,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_313]),c_0_115])]) ).
cnf(c_0_319,plain,
( hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),X1,tc_RealDef_Oreal),c_Orderings_Otop__class_Otop(tc_RealDef_Oreal)))
| ~ class_Lattices_Obounded__lattice(tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_314]),c_0_184])]) ).
cnf(c_0_320,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Obounded__lattice(X2) ),
clsarity_fun__Lattices_Obounded__lattice ).
cnf(c_0_321,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_315,c_0_316]),c_0_317]),c_0_115])]) ).
cnf(c_0_322,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(rw,[status(thm)],[c_0_318,c_0_312]) ).
cnf(c_0_323,negated_conjecture,
~ class_Lattices_Obounded__lattice(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_198,c_0_319]) ).
cnf(c_0_324,plain,
c_Set_Oimage(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X2),X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_168]),c_0_115])]) ).
cnf(c_0_325,negated_conjecture,
( tc_RealDef_Oreal = c_Orderings_Otop__class_Otop(tc_bool)
| class_Lattices_Obounded__lattice(c_Orderings_Otop__class_Otop(tc_bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_320,c_0_271]),c_0_205])]) ).
cnf(c_0_326,plain,
hBOOL(c_Lattices_Oupper__semilattice__class_Osup(tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_321,c_0_322]),c_0_115])]) ).
cnf(c_0_327,negated_conjecture,
~ class_Lattices_Obounded__lattice(c_Orderings_Otop__class_Otop(tc_bool)),
inference(rw,[status(thm)],[c_0_323,c_0_300]) ).
cnf(c_0_328,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_324,c_0_266]) ).
cnf(c_0_329,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| tc_RealDef_Oreal = X1
| class_Lattices_Obounded__lattice(X1) ),
inference(spm,[status(thm)],[c_0_325,c_0_185]) ).
cnf(c_0_330,plain,
c_Orderings_Otop__class_Otop(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(tc_bool),
inference(spm,[status(thm)],[c_0_108,c_0_326]) ).
cnf(c_0_331,negated_conjecture,
( tc_bool = X1
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(spm,[status(thm)],[c_0_327,c_0_301]) ).
cnf(c_0_332,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1) != tc_bool,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_328,c_0_312]),c_0_297]) ).
cnf(c_0_333,negated_conjecture,
( c_Lattices_Oupper__semilattice__class_Osup(tc_bool) = X1
| tc_bool = X1 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_329,c_0_297]),c_0_300]),c_0_330]),c_0_331]) ).
cnf(c_0_334,negated_conjecture,
( tc_bool = X1
| hAPP(X1,X2) != tc_bool ),
inference(spm,[status(thm)],[c_0_332,c_0_333]) ).
cnf(c_0_335,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
cls_Un__empty__right_0 ).
cnf(c_0_336,negated_conjecture,
$false,
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_334,c_0_335]),c_0_312]),c_0_332])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG349-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 03:39:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 26.74/26.97 % Version : CSE_E---1.5
% 26.74/26.97 % Problem : theBenchmark.p
% 26.74/26.97 % Proof found
% 26.74/26.97 % SZS status Theorem for theBenchmark.p
% 26.74/26.97 % SZS output start Proof
% See solution above
% 26.74/26.99 % Total time : 26.381000 s
% 26.74/26.99 % SZS output end Proof
% 26.74/26.99 % Total time : 26.391000 s
%------------------------------------------------------------------------------