TSTP Solution File: SCT019-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT019-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n015.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 : Thu Aug 31 14:10:45 EDT 2023
% Result : Unsatisfiable 41.18s 41.24s
% Output : CNFRefutation 41.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 182
% Syntax : Number of formulae : 400 ( 118 unt; 124 typ; 0 def)
% Number of atoms : 468 ( 194 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 389 ( 197 ~; 192 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 304 ( 116 >; 188 *; 0 +; 0 <<)
% Number of predicates : 35 ( 33 usr; 1 prp; 0-6 aty)
% Number of functors : 91 ( 91 usr; 8 con; 0-7 aty)
% Number of variables : 465 ( 177 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_23,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i ) > $i ).
tff(decl_24,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_25,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_26,type,
c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).
tff(decl_27,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_28,type,
tc_bool: $i ).
tff(decl_29,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_30,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
c_Set_Oinsert: ( $i * $i ) > $i ).
tff(decl_32,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_33,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: ( $i * $i * $i * $i ) > $i ).
tff(decl_34,type,
c_in: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
hBOOL: $i > $o ).
tff(decl_36,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i ) > $i ).
tff(decl_37,type,
c_Relation_Osym: ( $i * $i ) > $o ).
tff(decl_38,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_39,type,
c_Relation_ODomain: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
c_HOL_Ominus__class_Ominus: ( $i * $i ) > $i ).
tff(decl_41,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(decl_42,type,
c_Complete__Lattice_OSup__class_OSup: ( $i * $i ) > $i ).
tff(decl_43,type,
class_Orderings_Obot: $i > $o ).
tff(decl_44,type,
c_Relation_OImage: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
c_Wellfounded_Owf: ( $i * $i ) > $o ).
tff(decl_47,type,
c_Relation_ORange: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
c_Product__Type_OSigma: ( $i * $i * $i * $i ) > $i ).
tff(decl_50,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_51,type,
t_a: $i ).
tff(decl_52,type,
v_x: $i ).
tff(decl_53,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(decl_54,type,
c_Relation_OId__on: ( $i * $i ) > $i ).
tff(decl_55,type,
c_Relation_Orefl__on: ( $i * $i * $i ) > $o ).
tff(decl_56,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(decl_57,type,
c_Relation_Orel__comp: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_58,type,
c_List_Osko__Recdef__Xtfl__wf__induct__1__1: ( $i * $i * $i ) > $i ).
tff(decl_59,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_60,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_62,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1: ( $i * $i * $i ) > $i ).
tff(decl_63,type,
c_Wellfounded_Oacyclic: ( $i * $i ) > $o ).
tff(decl_64,type,
c_Relation_Oconverse: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_66,type,
c_Transitive__Closure_Otrancl: ( $i * $i ) > $i ).
tff(decl_67,type,
class_HOL_Ominus: $i > $o ).
tff(decl_68,type,
c_Wellfounded_Oacc: ( $i * $i ) > $i ).
tff(decl_69,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
c_List_Osko__Recdef__Xcuts__eq__1__1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_71,type,
c_Recdef_Ocut: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_72,type,
class_HOL_Oord: $i > $o ).
tff(decl_73,type,
class_Orderings_Otop: $i > $o ).
tff(decl_74,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_75,type,
c_Equiv__Relations_Oequiv: ( $i * $i * $i ) > $o ).
tff(decl_76,type,
c_Relation_OId: $i > $i ).
tff(decl_77,type,
c_Relation_Oirrefl: ( $i * $i ) > $o ).
tff(decl_78,type,
c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_79,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_80,type,
c_Relation_Oantisym: ( $i * $i ) > $o ).
tff(decl_81,type,
c_Relation_Osingle__valued: ( $i * $i * $i ) > $o ).
tff(decl_82,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_83,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_84,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
c_ATP__Linkup_Osko__Relation__XImageE__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_87,type,
c_ATP__Linkup_Osko__Relation__XImage__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_89,type,
c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_90,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1: ( $i * $i * $i ) > $i ).
tff(decl_91,type,
v_sko__Wellfounded__Xacc__Xinducts__1: ( $i * $i ) > $i ).
tff(decl_92,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1: ( $i * $i * $i ) > $i ).
tff(decl_93,type,
c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1: ( $i * $i * $i ) > $i ).
tff(decl_94,type,
v_sko__Wellfounded__Xacc__Xinduct__1: ( $i * $i ) > $i ).
tff(decl_95,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1: ( $i * $i * $i ) > $i ).
tff(decl_96,type,
c_Relation_Otrans: ( $i * $i ) > $o ).
tff(decl_97,type,
c_Relation_Ototal__on: ( $i * $i * $i ) > $o ).
tff(decl_98,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1: ( $i * $i ) > $i ).
tff(decl_99,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_100,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_101,type,
v_sko__Transitive__Closure__Xtrancl__Xcases__1: ( $i * $i * $i ) > $i ).
tff(decl_102,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_103,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_104,type,
c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_105,type,
c_ATP__Linkup_Osko__Relation__XIdE__1__1: ( $i * $i ) > $i ).
tff(decl_106,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1: ( $i * $i ) > $i ).
tff(decl_107,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1: ( $i * $i ) > $i ).
tff(decl_108,type,
c_ATP__Linkup_Osko__Relation__XId__onE__1__1: ( $i * $i * $i ) > $i ).
tff(decl_109,type,
v_r: $i ).
tff(decl_110,type,
t_b: $i ).
tff(decl_111,type,
c_Nitpick_Orefl_H: ( $i * $i ) > $o ).
tff(decl_112,type,
c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1: ( $i * $i ) > $i ).
tff(decl_113,type,
c_split: ( $i * $i * $i * $i ) > $i ).
tff(decl_114,type,
c_ATP__Linkup_Osko__Relation__XDomainE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_115,type,
c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_116,type,
c_ATP__Linkup_Osko__Relation__XRangeE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_117,type,
c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_118,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__1: ( $i * $i ) > $i ).
tff(decl_119,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__3: ( $i * $i ) > $i ).
tff(decl_120,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__2: ( $i * $i ) > $i ).
tff(decl_121,type,
c_Order__Relation_Ostrict__linear__order__on: ( $i * $i * $i ) > $o ).
tff(decl_122,type,
c_Relation_Oinv__image: ( $i * $i * $i * $i ) > $i ).
tff(decl_123,type,
c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2: ( $i * $i ) > $i ).
tff(decl_124,type,
c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1: ( $i * $i * $i ) > $i ).
tff(decl_125,type,
c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2: ( $i * $i * $i ) > $i ).
tff(decl_126,type,
c_Equiv__Relations_Ocongruent: ( $i * $i * $i * $i ) > $o ).
tff(decl_127,type,
c_Equiv__Relations_Ocongruent2: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_128,type,
c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1: ( $i * $i ) > $i ).
tff(decl_129,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1: ( $i * $i ) > $i ).
tff(decl_130,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2: ( $i * $i ) > $i ).
tff(decl_131,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3: ( $i * $i ) > $i ).
tff(decl_132,type,
c_FunDef_Oin__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_133,type,
c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1: $i > $i ).
tff(decl_134,type,
c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1: ( $i * $i ) > $i ).
tff(decl_135,type,
c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1: ( $i * $i ) > $i ).
tff(decl_136,type,
c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2: ( $i * $i ) > $i ).
tff(decl_137,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(decl_138,type,
c_Arrow__Order__Mirabelle_Omktop: ( $i * $i ) > $i ).
tff(decl_139,type,
c_Arrow__Order__Mirabelle_Omkbot: ( $i * $i ) > $i ).
tff(decl_140,type,
c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1: ( $i * $i ) > $i ).
tff(decl_141,type,
v_xa: $i ).
tff(decl_142,type,
v_F: $i > $i ).
tff(decl_143,type,
v_i: $i ).
tff(decl_144,type,
v_P: $i > $i ).
tff(decl_145,type,
c_fequal: ( $i * $i * $i ) > $o ).
cnf(cls_inf1E_1,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X4,tc_bool)),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
cnf(cls_inf__fun__eq_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),X1),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_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/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
cnf(cls_sup__top__left_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X1),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
cnf(cls_inf__sup__absorb_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
cnf(cls_mem__def_1,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(cls_UNIV__eq__I_0,axiom,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1),X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__eq__I_0) ).
cnf(cls_sup__top__right_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),X2)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
cnf(cls_fun__diff__def_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X2,v_x),X1),hAPP(X3,v_x))
| ~ class_HOL_Ominus(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
cnf(clsarity_bool__HOL_Ominus,axiom,
class_HOL_Ominus(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
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/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(cls_sup__idem_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(cls_Diff__UNIV_0,axiom,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
cnf(cls_Diff__insert__absorb_0,axiom,
( hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X1,X2),X3),tc_fun(X2,tc_bool)),hAPP(c_Set_Oinsert(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X3
| hBOOL(c_in(X1,X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
cnf(cls_irrefl__def_0,axiom,
( ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)))
| ~ c_Relation_Oirrefl(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_Relation_Oirrefl(hAPP(v_xa,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_irrefl__def_1,axiom,
( c_Relation_Oirrefl(X1,X2)
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),X2,X2),X1,tc_prod(X2,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_1) ).
cnf(cls_conjecture_5,negated_conjecture,
( c_Relation_Oirrefl(v_F(X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Relation_Otrans(hAPP(v_xa,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_xa,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X3,tc_bool)),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
cnf(cls_pair__in__Id__conv_1,axiom,
hBOOL(c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).
cnf(cls_emptyE_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
cnf(cls_not__acc__down_0,axiom,
( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X2,X3),X2,X3,X3),X1,tc_prod(X3,X3)))
| hBOOL(c_in(X2,c_Wellfounded_Oacc(X1,X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
cnf(cls_INF__leI_0,axiom,
( c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X3,X4,X1),hAPP(X3,X5),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(c_in(X5,X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__leI_0) ).
cnf(cls_Int__UNIV__left_0,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
cnf(cls_INF__const_0,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,c_COMBK(X3,X1,X4),X4,X1) = X3
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__const_0) ).
cnf(cls_predicate1D_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
cnf(clsarity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
cnf(cls_DiffE_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X3,tc_bool)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
cnf(cls_Diff__disjoint_0,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),X1)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
cnf(cls_Int__insert__left_1,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Set_Oinsert(X1,X2),X3),tc_fun(X2,tc_bool)),X4) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X2,tc_bool)),X4)
| hBOOL(c_in(X1,X4,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
cnf(cls_insert__absorb_0,axiom,
( hAPP(c_Set_Oinsert(X1,X2),X3) = X3
| ~ hBOOL(c_in(X1,X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_conjecture_3,negated_conjecture,
v_F(v_xa) != hAPP(v_xa,v_i),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_sup__fun__eq_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(X2,v_x),X1),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
cnf(cls_Un__Diff__cancel_0,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),X1)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
cnf(cls_Un__empty__right_0,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(clsarity_fun__Lattices_Oupper__semilattice,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
cnf(cls_in__mkbot_0,axiom,
~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
cnf(cls_Diff__empty_0,axiom,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
cnf(cls_bex__UNIV_2,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X1,X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UNIV_2) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
cnf(cls_inf__top__left_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X1),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X2)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
cnf(cls_inf__sup__aci_I3_J_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X4))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
cnf(cls_inf__bot__left_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X1),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(c_Set_Oinsert(X2,X1),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
cnf(c_0_58,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X4,tc_bool)),X1),X2)) ),
cls_inf1E_1 ).
cnf(c_0_59,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),X1),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__fun__eq_0 ).
cnf(c_0_60,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_61,plain,
( hBOOL(hAPP(X1,v_x))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),tc_bool),hAPP(X1,v_x))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]) ).
cnf(c_0_62,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_63,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_64,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_65,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),tc_bool),X1)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X1),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__left_0 ).
cnf(c_0_67,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_68,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_69,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_bool),X1)) ),
inference(spm,[status(thm)],[c_0_65,c_0_62]) ).
cnf(c_0_71,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__absorb_0 ).
cnf(c_0_72,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X2,X1)) ),
cls_mem__def_1 ).
cnf(c_0_73,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X1) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_74,plain,
hBOOL(c_Orderings_Otop__class_Otop(tc_bool)),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2))
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_60])]) ).
cnf(c_0_76,axiom,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1),X2,X1)) ),
cls_UNIV__eq__I_0 ).
cnf(c_0_77,plain,
hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]) ).
cnf(c_0_78,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),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_79,plain,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3)),
inference(spm,[status(thm)],[c_0_72,c_0_68]) ).
cnf(c_0_80,plain,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),X3))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_75]) ).
cnf(c_0_81,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),X2)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I5_J_0 ).
cnf(c_0_82,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_83,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_78,c_0_67]) ).
cnf(c_0_84,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X2,v_x),X1),hAPP(X3,v_x))
| ~ class_HOL_Ominus(X1) ),
cls_fun__diff__def_0 ).
cnf(c_0_85,axiom,
class_HOL_Ominus(tc_bool),
clsarity_bool__HOL_Ominus ).
cnf(c_0_86,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_87,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_88,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_76,c_0_79]) ).
cnf(c_0_89,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__idem_0 ).
cnf(c_0_90,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool)
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_80]) ).
cnf(c_0_91,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = c_Orderings_Otop__class_Otop(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]),c_0_60])]) ).
cnf(c_0_92,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_93,plain,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(t_a,tc_bool)),X2),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),tc_bool),hAPP(X2,v_x)),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_94,axiom,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_Diff__UNIV_0 ).
cnf(c_0_95,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_96,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),v_x) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_69,c_0_88]) ).
cnf(c_0_97,axiom,
( hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X1,X2),X3),tc_fun(X2,tc_bool)),hAPP(c_Set_Oinsert(X1,X2),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X3
| hBOOL(c_in(X1,X3,X2)) ),
cls_Diff__insert__absorb_0 ).
cnf(c_0_98,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = X1
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_92])]) ).
cnf(c_0_99,axiom,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1)),
cls_insert__code_1 ).
cnf(c_0_100,plain,
hAPP(c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]),c_0_96]) ).
cnf(c_0_101,plain,
( hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1,t_a),X2),v_x),tc_bool),hAPP(hAPP(c_Set_Oinsert(X1,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x)) = hAPP(X2,v_x)
| hBOOL(c_in(X1,X2,t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_97]),c_0_85])]) ).
cnf(c_0_102,plain,
c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_103,plain,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_100,c_0_62]) ).
cnf(c_0_104,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,X1,X3)) ),
cls_mem__def_0 ).
cnf(c_0_105,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(X1,v_x)
| hBOOL(c_in(v_x,X1,t_a)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]) ).
cnf(c_0_106,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(X1,v_x)
| hBOOL(hAPP(X1,v_x)) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_107,axiom,
( ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)))
| ~ c_Relation_Oirrefl(X3,X2) ),
cls_irrefl__def_0 ).
cnf(c_0_108,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_62]) ).
cnf(c_0_109,negated_conjecture,
c_Relation_Oirrefl(hAPP(v_xa,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_1 ).
cnf(c_0_110,axiom,
( c_Relation_Oirrefl(X1,X2)
| hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),X2,X2),X1,tc_prod(X2,X2))) ),
cls_irrefl__def_1 ).
cnf(c_0_111,plain,
~ c_Relation_Oirrefl(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X1),
inference(spm,[status(thm)],[c_0_107,c_0_77]) ).
cnf(c_0_112,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| c_Orderings_Otop__class_Otop(tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_98,c_0_108]) ).
cnf(c_0_113,plain,
( ~ c_Relation_Oirrefl(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_107,c_0_80]) ).
cnf(c_0_114,negated_conjecture,
( c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_bool),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(hAPP(v_xa,X1)) ),
inference(spm,[status(thm)],[c_0_109,c_0_98]) ).
cnf(c_0_115,plain,
( c_Relation_Oirrefl(X1,X2)
| hBOOL(hAPP(X1,c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X1,X2),X2,X2))) ),
inference(spm,[status(thm)],[c_0_104,c_0_110]) ).
cnf(c_0_116,negated_conjecture,
( c_Relation_Oirrefl(v_F(X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt) ),
cls_conjecture_5 ).
cnf(c_0_117,negated_conjecture,
c_Relation_Otrans(hAPP(v_xa,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_0 ).
cnf(c_0_118,negated_conjecture,
c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_xa,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_2 ).
cnf(c_0_119,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_bool),X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_120,plain,
( X1 = X2
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_98]) ).
cnf(c_0_121,plain,
( ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_bool),X1)
| ~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_113,c_0_98]) ).
cnf(c_0_122,negated_conjecture,
( c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_bool),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Oirrefl(v_xa,X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_123,negated_conjecture,
c_Relation_Oirrefl(v_F(v_xa),tc_Arrow__Order__Mirabelle_Oalt),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]),c_0_109])]) ).
cnf(c_0_124,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ c_Relation_Oirrefl(X1,X2)
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_74])]) ).
cnf(c_0_125,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(X3,tc_bool))
| ~ hBOOL(X3)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_98]) ).
cnf(c_0_126,negated_conjecture,
( c_Relation_Oirrefl(v_xa,X1)
| ~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_127,negated_conjecture,
( v_F(v_xa) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_bool),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(spm,[status(thm)],[c_0_123,c_0_112]) ).
cnf(c_0_128,negated_conjecture,
( c_Lattices_Oupper__semilattice__class_Osup(v_F(v_xa),tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(v_F(v_xa)) ),
inference(spm,[status(thm)],[c_0_124,c_0_123]) ).
cnf(c_0_129,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)))
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_82]),c_0_74])]) ).
cnf(c_0_130,negated_conjecture,
( c_Relation_Oirrefl(v_xa,X1)
| ~ hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_82]),c_0_74])]) ).
cnf(c_0_131,negated_conjecture,
( v_F(v_xa) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_127]) ).
cnf(c_0_132,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| ~ c_Relation_Oirrefl(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_133,negated_conjecture,
( c_Lattices_Oupper__semilattice__class_Osup(v_F(v_xa),tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| v_F(v_xa) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_128,c_0_108]) ).
cnf(c_0_134,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_129,c_0_82]) ).
cnf(c_0_135,negated_conjecture,
( c_Relation_Oirrefl(v_xa,X1)
| ~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool)) ),
inference(spm,[status(thm)],[c_0_130,c_0_82]) ).
cnf(c_0_136,negated_conjecture,
( v_F(v_xa) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_82]),c_0_74])]) ).
cnf(c_0_137,negated_conjecture,
( v_F(v_xa) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),X1) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_138,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ c_Relation_Oirrefl(X1,X2)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_134,c_0_108]) ).
cnf(c_0_139,negated_conjecture,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Relation_Oirrefl(v_xa,X1) ),
inference(spm,[status(thm)],[c_0_135,c_0_108]) ).
cnf(c_0_140,negated_conjecture,
( v_F(v_xa) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool)) ),
inference(spm,[status(thm)],[c_0_136,c_0_82]) ).
cnf(c_0_141,negated_conjecture,
( v_F(v_xa) = X1
| hBOOL(X1)
| ~ c_Relation_Oirrefl(X1,X2) ),
inference(spm,[status(thm)],[c_0_137,c_0_108]) ).
cnf(c_0_142,negated_conjecture,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(v_xa) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_143,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X3,tc_bool)),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_disjoint__iff__not__equal_0 ).
cnf(c_0_144,negated_conjecture,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| v_F(v_xa) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_112]),c_0_74])]) ).
cnf(c_0_145,negated_conjecture,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| v_F(v_xa) = v_xa ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_139]),c_0_142]) ).
cnf(c_0_146,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X2,tc_bool)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(X4,X3,X2)) ),
inference(spm,[status(thm)],[c_0_143,c_0_79]) ).
cnf(c_0_147,axiom,
hBOOL(c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2))),
cls_pair__in__Id__conv_1 ).
cnf(c_0_148,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
cls_emptyE_0 ).
cnf(c_0_149,axiom,
( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X2,X3),X2,X3,X3),X1,tc_prod(X3,X3)))
| hBOOL(c_in(X2,c_Wellfounded_Oacc(X1,X3),X3)) ),
cls_not__acc__down_0 ).
cnf(c_0_150,negated_conjecture,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) = v_xa ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_151,axiom,
( c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X3,X4,X1),hAPP(X3,X5),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(c_in(X5,X2,X4)) ),
cls_INF__leI_0 ).
cnf(c_0_152,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_153,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2) = X2,
cls_Int__UNIV__left_0 ).
cnf(c_0_154,plain,
hBOOL(c_in(X1,c_Wellfounded_Oacc(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2)),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_155,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_bool) = v_xa
| ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_150]),c_0_74])]) ).
cnf(c_0_156,plain,
( c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Relation_OId(X1),X2,tc_prod(X1,X1),X3),hAPP(X2,c_Pair(X4,X4,X1,X1)),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(spm,[status(thm)],[c_0_151,c_0_147]) ).
cnf(c_0_157,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,c_COMBK(X3,X1,X4),X4,X1) = X3
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
cls_INF__const_0 ).
cnf(c_0_158,plain,
c_Relation_OId(X1) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_159,plain,
c_Wellfounded_Oacc(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_76,c_0_154]) ).
cnf(c_0_160,negated_conjecture,
( X1 = v_xa
| hBOOL(X1)
| ~ c_Relation_Oirrefl(X1,X2) ),
inference(spm,[status(thm)],[c_0_155,c_0_108]) ).
cnf(c_0_161,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
cls_predicate1D_0 ).
cnf(c_0_162,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_62]),c_0_158]) ).
cnf(c_0_163,axiom,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
clsarity_fun__Complete__Lattice_Ocomplete__lattice ).
cnf(c_0_164,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X3,tc_bool)),X2),X3)) ),
cls_DiffE_1 ).
cnf(c_0_165,plain,
hBOOL(c_in(X1,hAPP(c_Set_Oinsert(X1,X2),X3),X4)),
inference(spm,[status(thm)],[c_0_72,c_0_99]) ).
cnf(c_0_166,plain,
c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) = c_Orderings_Otop__class_Otop(tc_bool),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_154]),c_0_159]) ).
cnf(c_0_167,negated_conjecture,
( v_F(v_xa) = v_xa
| hBOOL(v_F(v_xa)) ),
inference(spm,[status(thm)],[c_0_160,c_0_123]) ).
cnf(c_0_168,plain,
( hBOOL(hAPP(X1,X2))
| ~ class_Lattices_Oupper__semilattice(X3)
| ~ hBOOL(X2)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3),X1,tc_fun(X4,tc_bool)) ),
inference(spm,[status(thm)],[c_0_161,c_0_89]) ).
cnf(c_0_169,plain,
( c_lessequals(X1,X1,tc_fun(X2,X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_170,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
clsarity_bool__Complete__Lattice_Ocomplete__lattice ).
cnf(c_0_171,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),X1)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_Diff__disjoint_0 ).
cnf(c_0_172,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Set_Oinsert(X1,X2),X3),tc_fun(X2,tc_bool)),X4) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X2,tc_bool)),X4)
| hBOOL(c_in(X1,X4,X2)) ),
cls_Int__insert__left_1 ).
cnf(c_0_173,plain,
~ hBOOL(c_in(X1,hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(X3,tc_bool)),hAPP(c_Set_Oinsert(X1,X4),X5)),X3)),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_174,axiom,
( hAPP(c_Set_Oinsert(X1,X2),X3) = X3
| ~ hBOOL(c_in(X1,X3,X2)) ),
cls_insert__absorb_0 ).
cnf(c_0_175,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_166,c_0_88]) ).
cnf(c_0_176,negated_conjecture,
v_F(v_xa) != hAPP(v_xa,v_i),
cls_conjecture_3 ).
cnf(c_0_177,negated_conjecture,
( v_F(v_xa) = c_Orderings_Otop__class_Otop(tc_bool)
| v_F(v_xa) = v_xa ),
inference(spm,[status(thm)],[c_0_98,c_0_167]) ).
cnf(c_0_178,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(X2,v_x),X1),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
cls_sup__fun__eq_0 ).
cnf(c_0_179,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2),X1))
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_170])]) ).
cnf(c_0_180,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X2,tc_bool)),X3) = X3,
inference(spm,[status(thm)],[c_0_153,c_0_88]) ).
cnf(c_0_181,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),hAPP(c_Set_Oinsert(X4,X2),X1))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_173]) ).
cnf(c_0_182,plain,
hAPP(c_Set_Oinsert(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_74])]) ).
cnf(c_0_183,negated_conjecture,
( X1 != hAPP(v_xa,v_i)
| ~ hBOOL(v_F(v_xa))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_176,c_0_120]) ).
cnf(c_0_184,negated_conjecture,
( v_F(v_xa) = v_xa
| c_Orderings_Otop__class_Otop(tc_bool) != v_xa ),
inference(ef,[status(thm)],[c_0_177]) ).
cnf(c_0_185,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(t_a,tc_bool)),X2),v_x) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(X1,v_x),tc_bool),hAPP(X2,v_x)),
inference(spm,[status(thm)],[c_0_178,c_0_60]) ).
cnf(c_0_186,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2),X1)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_179]) ).
cnf(c_0_187,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X1) = X1,
inference(spm,[status(thm)],[c_0_89,c_0_92]) ).
cnf(c_0_188,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X3,tc_fun(X2,tc_bool)),X1)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),X3),
cls_Un__Diff__cancel_0 ).
cnf(c_0_189,plain,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_182]) ).
cnf(c_0_190,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X1,
cls_Un__empty__right_0 ).
cnf(c_0_191,negated_conjecture,
( v_F(v_xa) = c_Orderings_Obot__class_Obot(tc_bool)
| X1 != hAPP(v_xa,v_i)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_183,c_0_108]) ).
cnf(c_0_192,negated_conjecture,
( v_F(v_xa) = v_xa
| c_Orderings_Obot__class_Obot(tc_bool) = X1
| X1 != v_xa ),
inference(spm,[status(thm)],[c_0_184,c_0_112]) ).
cnf(c_0_193,plain,
( hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = hAPP(X1,v_x)
| ~ class_Lattices_Oupper__semilattice(tc_fun(t_a,tc_bool))
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_187]) ).
cnf(c_0_194,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
clsarity_fun__Lattices_Oupper__semilattice ).
cnf(c_0_195,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X2,tc_bool)),X3) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_190]) ).
cnf(c_0_196,plain,
~ c_Relation_Oirrefl(c_Relation_OId(X1),X1),
inference(spm,[status(thm)],[c_0_107,c_0_147]) ).
cnf(c_0_197,negated_conjecture,
( v_F(v_xa) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(hAPP(v_xa,v_i)) ),
inference(er,[status(thm)],[c_0_191]) ).
cnf(c_0_198,negated_conjecture,
( hAPP(v_xa,X1) = v_xa
| hBOOL(hAPP(v_xa,X1)) ),
inference(spm,[status(thm)],[c_0_160,c_0_109]) ).
cnf(c_0_199,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_bool) = v_xa
| v_F(v_xa) = v_xa ),
inference(er,[status(thm)],[c_0_192]) ).
cnf(c_0_200,plain,
( hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = hAPP(X1,v_x)
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_194]),c_0_60])]) ).
cnf(c_0_201,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) ),
inference(spm,[status(thm)],[c_0_106,c_0_195]) ).
cnf(c_0_202,plain,
( c_Relation_OId(X1) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_bool),X1) ),
inference(spm,[status(thm)],[c_0_196,c_0_112]) ).
cnf(c_0_203,negated_conjecture,
( hAPP(v_xa,v_i) = v_xa
| v_F(v_xa) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_204,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_bool) = v_xa
| hAPP(v_xa,v_i) != v_xa ),
inference(spm,[status(thm)],[c_0_176,c_0_199]) ).
cnf(c_0_205,plain,
~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2),
inference(spm,[status(thm)],[c_0_107,c_0_79]) ).
cnf(c_0_206,plain,
( hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = c_Orderings_Otop__class_Otop(tc_bool)
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_201]),c_0_91]) ).
cnf(c_0_207,negated_conjecture,
( v_F(v_xa) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_202,c_0_127]) ).
cnf(c_0_208,negated_conjecture,
c_Orderings_Obot__class_Obot(tc_bool) = v_xa,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_203]),c_0_204]) ).
cnf(c_0_209,plain,
( hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = c_Orderings_Otop__class_Otop(tc_bool)
| ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),X1) ),
inference(spm,[status(thm)],[c_0_205,c_0_206]) ).
cnf(c_0_210,negated_conjecture,
( c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),tc_Arrow__Order__Mirabelle_Oalt) ),
inference(spm,[status(thm)],[c_0_123,c_0_207]) ).
cnf(c_0_211,negated_conjecture,
( v_F(v_xa) = v_xa
| X1 != hAPP(v_xa,v_i)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_183,c_0_167]) ).
cnf(c_0_212,plain,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2) = c_Orderings_Otop__class_Otop(tc_bool)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_90]) ).
cnf(c_0_213,negated_conjecture,
( c_Lattices_Oupper__semilattice__class_Osup(v_F(v_xa),tc_bool) = v_xa
| v_F(v_xa) = v_xa ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_208]),c_0_208]) ).
cnf(c_0_214,plain,
( v_xa = X1
| hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_108,c_0_208]) ).
cnf(c_0_215,axiom,
~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
cls_in__mkbot_0 ).
cnf(c_0_216,negated_conjecture,
( hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = c_Orderings_Otop__class_Otop(tc_bool)
| c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_209,c_0_210]) ).
cnf(c_0_217,negated_conjecture,
( v_F(v_xa) = v_xa
| ~ hBOOL(hAPP(v_xa,v_i)) ),
inference(er,[status(thm)],[c_0_211]) ).
cnf(c_0_218,negated_conjecture,
( v_F(v_xa) = v_xa
| c_Orderings_Otop__class_Otop(tc_bool) != hAPP(v_xa,v_i) ),
inference(spm,[status(thm)],[c_0_176,c_0_177]) ).
cnf(c_0_219,negated_conjecture,
( hAPP(v_xa,X1) = c_Orderings_Otop__class_Otop(tc_bool)
| v_F(v_xa) = v_xa ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_214]) ).
cnf(c_0_220,plain,
hBOOL(c_in(X1,c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X2,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
inference(spm,[status(thm)],[c_0_215,c_0_149]) ).
cnf(c_0_221,negated_conjecture,
( hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = c_Orderings_Otop__class_Otop(tc_bool)
| c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt) = v_xa ),
inference(rw,[status(thm)],[c_0_216,c_0_208]) ).
cnf(c_0_222,negated_conjecture,
( hAPP(v_xa,v_i) = v_xa
| v_F(v_xa) = v_xa ),
inference(spm,[status(thm)],[c_0_217,c_0_198]) ).
cnf(c_0_223,negated_conjecture,
( v_F(v_xa) = v_xa
| hAPP(v_xa,X1) != hAPP(v_xa,v_i) ),
inference(spm,[status(thm)],[c_0_218,c_0_219]) ).
cnf(c_0_224,axiom,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X1,
cls_Diff__empty_0 ).
cnf(c_0_225,plain,
hBOOL(hAPP(c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),X2)),
inference(spm,[status(thm)],[c_0_104,c_0_220]) ).
cnf(c_0_226,negated_conjecture,
( hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = c_Orderings_Otop__class_Otop(tc_bool)
| ~ c_Relation_Oirrefl(v_xa,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(spm,[status(thm)],[c_0_196,c_0_221]) ).
cnf(c_0_227,negated_conjecture,
( hAPP(v_xa,v_i) = v_xa
| c_Relation_Oirrefl(v_xa,tc_Arrow__Order__Mirabelle_Oalt) ),
inference(spm,[status(thm)],[c_0_123,c_0_222]) ).
cnf(c_0_228,negated_conjecture,
v_F(v_xa) = v_xa,
inference(er,[status(thm)],[c_0_223]) ).
cnf(c_0_229,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X1,X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
cls_bex__UNIV_2 ).
cnf(c_0_230,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_231,plain,
hAPP(c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = hAPP(X1,v_x),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_224]),c_0_85])]),c_0_95]) ).
cnf(c_0_232,plain,
hAPP(c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),X2) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_98,c_0_225]) ).
cnf(c_0_233,negated_conjecture,
( hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = c_Orderings_Otop__class_Otop(tc_bool)
| hAPP(v_xa,v_i) = v_xa ),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_234,negated_conjecture,
hAPP(v_xa,v_i) != v_xa,
inference(rw,[status(thm)],[c_0_176,c_0_228]) ).
cnf(c_0_235,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_95]),c_0_230]) ).
cnf(c_0_236,plain,
hAPP(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_231,c_0_232]) ).
cnf(c_0_237,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ hBOOL(hAPP(X2,X3))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_230,c_0_120]) ).
cnf(c_0_238,negated_conjecture,
hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x) = c_Orderings_Otop__class_Otop(tc_bool),
inference(sr,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_239,plain,
~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X1,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_95]),c_0_235]) ).
cnf(c_0_240,plain,
hBOOL(c_in(c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_236]),c_0_74])]) ).
cnf(c_0_241,negated_conjecture,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_238]),c_0_74])]) ).
cnf(c_0_242,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = X1
| v_xa = X1 ),
inference(rw,[status(thm)],[c_0_112,c_0_208]) ).
cnf(c_0_243,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X1),X1),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__top__left_0 ).
cnf(c_0_244,plain,
~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))),
inference(spm,[status(thm)],[c_0_239,c_0_62]) ).
cnf(c_0_245,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X2)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I1_J_0 ).
cnf(c_0_246,plain,
c_in(c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X1) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_98,c_0_240]) ).
cnf(c_0_247,negated_conjecture,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = v_xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_242]),c_0_74])]) ).
cnf(c_0_248,plain,
hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_83]),c_0_74])]) ).
cnf(c_0_249,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X1) = X1,
inference(spm,[status(thm)],[c_0_243,c_0_67]) ).
cnf(c_0_250,plain,
~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_245]),c_0_60])]) ).
cnf(c_0_251,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X4))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I3_J_0 ).
cnf(c_0_252,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X1),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__bot__left_0 ).
cnf(c_0_253,plain,
( hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),X1))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_99,c_0_98]) ).
cnf(c_0_254,plain,
hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),X1),c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_246]),c_0_74])]) ).
cnf(c_0_255,plain,
c_Relation_OId(X1) != v_xa,
inference(rw,[status(thm)],[c_0_158,c_0_247]) ).
cnf(c_0_256,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(c_Set_Oinsert(X2,X1),X3),
cls_empty__not__insert_0 ).
cnf(c_0_257,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),tc_fun(X2,tc_bool)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(c_in(c_Orderings_Otop__class_Otop(tc_bool),X3,X2)) ),
inference(spm,[status(thm)],[c_0_143,c_0_248]) ).
cnf(c_0_258,plain,
( hBOOL(c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X2))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_249]) ).
cnf(c_0_259,plain,
~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_251]),c_0_60])]) ).
cnf(c_0_260,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_252,c_0_67]) ).
cnf(c_0_261,plain,
( hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)))
| ~ hBOOL(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool)) ),
inference(spm,[status(thm)],[c_0_253,c_0_254]) ).
cnf(c_0_262,plain,
c_Orderings_Otop__class_Otop(tc_bool) != v_xa,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_242]),c_0_255]) ).
cnf(c_0_263,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),
inference(spm,[status(thm)],[c_0_256,c_0_254]) ).
cnf(c_0_264,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_258]),c_0_74])]) ).
cnf(c_0_265,plain,
( ~ hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)))
| ~ hBOOL(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_98]),c_0_260]) ).
cnf(c_0_266,plain,
( hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_xa))
| ~ hBOOL(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool)) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261,c_0_242]),c_0_208]),c_0_262]) ).
cnf(c_0_267,plain,
c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool) != v_xa,
inference(rw,[status(thm)],[c_0_263,c_0_247]) ).
cnf(c_0_268,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_264,c_0_82]) ).
cnf(c_0_269,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_xa))
| ~ hBOOL(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool)) ),
inference(spm,[status(thm)],[c_0_265,c_0_208]) ).
cnf(c_0_270,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_xa)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_266,c_0_242]),c_0_74])]),c_0_267]) ).
cnf(c_0_271,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_268,c_0_153]) ).
cnf(c_0_272,negated_conjecture,
~ hBOOL(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_269,c_0_270])]) ).
cnf(c_0_273,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool) != v_xa,
inference(rw,[status(thm)],[c_0_271,c_0_247]) ).
cnf(c_0_274,negated_conjecture,
c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool) = v_xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_242]),c_0_74])]) ).
cnf(c_0_275,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_273,c_0_274])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT019-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 16:04:51 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.56 start to proof: theBenchmark
% 41.18/41.24 % Version : CSE_E---1.5
% 41.18/41.24 % Problem : theBenchmark.p
% 41.18/41.24 % Proof found
% 41.18/41.24 % SZS status Theorem for theBenchmark.p
% 41.18/41.24 % SZS output start Proof
% See solution above
% 41.18/41.26 % Total time : 40.647000 s
% 41.18/41.26 % SZS output end Proof
% 41.18/41.26 % Total time : 40.673000 s
%------------------------------------------------------------------------------