TSTP Solution File: SCT020-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT020-1 : 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 : n006.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 14:10:46 EDT 2023
% Result : Unsatisfiable 78.67s 78.87s
% Output : CNFRefutation 78.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 191
% Syntax : Number of formulae : 364 ( 124 unt; 126 typ; 0 def)
% Number of atoms : 387 ( 112 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 293 ( 144 ~; 149 |; 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 : 93 ( 93 usr; 10 con; 0-7 aty)
% Number of variables : 523 ( 206 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_P: $i ).
tff(decl_142,type,
v_a: $i ).
tff(decl_143,type,
v_b: $i ).
tff(decl_144,type,
v_F: $i > $i ).
tff(decl_145,type,
v_i: $i ).
tff(decl_146,type,
v_Pa: $i > $i ).
tff(decl_147,type,
c_fequal: ( $i * $i * $i ) > $o ).
cnf(cls_inf1I_0,axiom,
( hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X1,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
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_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_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_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_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_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_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_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_subset__UNIV_0,axiom,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
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_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_le__funD_0,axiom,
( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
| ~ class_HOL_Oord(X1)
| ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
cnf(cls_bex__UNIV_0,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X1,X2)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UNIV_0) ).
cnf(cls_UNIV__I_0,axiom,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
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_le__sup__iff_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X1),X2),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
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_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_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_ball__UNIV_2,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2(X1,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__UNIV_2) ).
cnf(cls_sup__absorb1_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_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(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(cls_Image__Id_0,axiom,
hAPP(c_Relation_OImage(c_Relation_OId(X1),X1,X1),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).
cnf(cls_insert__iff_1,axiom,
hBOOL(c_in(X1,hAPP(c_Set_Oinsert(X1,X2),X3),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
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_order__eq__iff_2,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(cls_inf__absorb2_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
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(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/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
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_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_conjecture_3,negated_conjecture,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
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(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_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_2,negated_conjecture,
c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
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(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_conjecture_6,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_6) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_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_Int__insert__right_1,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_Set_Oinsert(X3,X2),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X4)
| hBOOL(c_in(X3,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
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_rtrancl_Ortrancl__refl_0,axiom,
hBOOL(c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
cnf(cls_le__infE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
cnf(cls_inf__bot__right_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
cnf(cls_le__iff__inf_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
cnf(cls_Domain__iff_1,axiom,
( hBOOL(c_in(X1,c_Relation_ODomain(X2,X3,X4),X3))
| ~ hBOOL(c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).
cnf(cls_trancl__id_0,axiom,
( c_Transitive__Closure_Otrancl(X1,X2) = X1
| ~ c_Relation_Otrans(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__id_0) ).
cnf(cls_trancl__unfold__left_0,axiom,
c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
cnf(cls_rtrancl__reflcl_0,axiom,
c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).
cnf(cls_Un__empty__left_0,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
cnf(cls_trans__Id_0,axiom,
c_Relation_Otrans(c_Relation_OId(X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id_0) ).
cnf(cls_Id__O__R_0,axiom,
c_Relation_Orel__comp(c_Relation_OId(X1),X2,X1,X1,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
cnf(cls_UNIV__not__empty_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
cnf(cls_pair__in__Id__conv_0,axiom,
( X1 = X2
| ~ hBOOL(c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId(X3),tc_prod(X3,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).
cnf(c_0_65,axiom,
( hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X1,X4)) ),
cls_inf1I_0 ).
cnf(c_0_66,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_67,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_68,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(X2,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(X3,X4)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_69,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_70,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_71,axiom,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1)),
cls_insert__code_1 ).
cnf(c_0_72,plain,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_73,plain,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(hAPP(c_Set_Oinsert(X1,X2),X3),X4))),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_74,plain,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(hAPP(c_Set_Oinsert(X1,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X4))) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_75,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
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_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3)),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_78,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_79,axiom,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
cls_subset__UNIV_0 ).
cnf(c_0_80,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_77]) ).
cnf(c_0_81,plain,
( hBOOL(c_in(X1,c_COMBK(X2,X3,X4),X5))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_78]) ).
cnf(c_0_82,plain,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_83,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_COMBK(X2,X3,X4)
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_81]) ).
cnf(c_0_84,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_85,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_86,axiom,
( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
| ~ class_HOL_Oord(X1)
| ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
cls_le__funD_0 ).
cnf(c_0_87,plain,
( c_lessequals(X1,c_COMBK(X2,X3,X4),tc_fun(X5,tc_bool))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_88,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord ).
cnf(c_0_89,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X1,X2)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)) ),
cls_bex__UNIV_0 ).
cnf(c_0_90,axiom,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)),
cls_UNIV__I_0 ).
cnf(c_0_91,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,X1,X3)) ),
cls_mem__def_0 ).
cnf(c_0_92,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_84,c_0_85]) ).
cnf(c_0_93,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X1),X2),X3,X1) ),
cls_le__sup__iff_1 ).
cnf(c_0_94,plain,
( c_lessequals(hAPP(X1,X2),X3,tc_bool)
| ~ hBOOL(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_78]),c_0_88])]) ).
cnf(c_0_95,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_96,axiom,
( hAPP(c_Set_Oinsert(X1,X2),X3) = X3
| ~ hBOOL(c_in(X1,X3,X2)) ),
cls_insert__absorb_0 ).
cnf(c_0_97,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X2,X1)) ),
cls_mem__def_1 ).
cnf(c_0_98,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X1,X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90])]) ).
cnf(c_0_99,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_91,c_0_92]) ).
cnf(c_0_100,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2(X1,X3))) ),
cls_ball__UNIV_2 ).
cnf(c_0_101,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_sup__absorb1_0 ).
cnf(c_0_102,plain,
( c_lessequals(X1,X2,tc_bool)
| ~ hBOOL(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95])]) ).
cnf(c_0_103,plain,
( hAPP(c_Set_Oinsert(X1,X2),X3) = X3
| ~ hBOOL(hAPP(X3,X1)) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_104,plain,
hBOOL(hAPP(c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),X3))),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_105,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2(X1,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_90])]) ).
cnf(c_0_106,plain,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2) = X1
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_95])]) ).
cnf(c_0_107,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_108,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_109,axiom,
hAPP(c_Relation_OImage(c_Relation_OId(X1),X1,X1),X2) = X2,
cls_Image__Id_0 ).
cnf(c_0_110,axiom,
hBOOL(c_in(X1,hAPP(c_Set_Oinsert(X1,X2),X3),X2)),
cls_insert__iff_1 ).
cnf(c_0_111,plain,
hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),X3),X4),c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt)) = c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_112,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_113,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),X1),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_114,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_115,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_116,plain,
( hBOOL(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Relation_OImage(c_Relation_OId(X1),X1,X1),X2))
| ~ hBOOL(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_109]),c_0_109]) ).
cnf(c_0_117,plain,
hBOOL(c_in(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),X3),c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),tc_Arrow__Order__Mirabelle_Oalt),X4)),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_118,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__eq__iff_2 ).
cnf(c_0_119,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_120,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_121,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_inf__absorb2_0 ).
cnf(c_0_122,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_123,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_124,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_114,c_0_115]) ).
cnf(c_0_125,plain,
( hBOOL(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_Relation_OImage(c_Relation_OId(X1),X1,X1),X2))
| ~ hBOOL(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_109]),c_0_109]) ).
cnf(c_0_126,plain,
hBOOL(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Relation_OImage(c_Relation_OId(X1),X1,X1),X2)),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_127,plain,
( X1 = X2
| ~ hBOOL(X1)
| ~ c_lessequals(X1,X2,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_102]),c_0_119])]) ).
cnf(c_0_128,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_129,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
clsarity_bool__Complete__Lattice_Ocomplete__lattice ).
cnf(c_0_130,plain,
( hAPP(c_Set_Oinsert(X1,X2),c_Lattices_Oupper__semilattice__class_Osup(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X3,tc_bool)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_103,c_0_120]) ).
cnf(c_0_131,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X2) = X2
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_102]),c_0_122])]) ).
cnf(c_0_132,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(t_a,tc_bool)),X2),v_x) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X1,v_x),tc_bool),hAPP(X2,v_x)),
inference(spm,[status(thm)],[c_0_123,c_0_108]) ).
cnf(c_0_133,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_134,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_135,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_124,c_0_80]) ).
cnf(c_0_136,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2)))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_70,c_0_120]) ).
cnf(c_0_137,plain,
hBOOL(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_Relation_OImage(c_Relation_OId(X1),X1,X1),X2)),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_138,plain,
( X1 = c_Complete__Lattice_OSup__class_OSup(X2,tc_bool)
| ~ hBOOL(c_in(X1,X2,tc_bool))
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129])]) ).
cnf(c_0_139,plain,
( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),X3))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_130]) ).
cnf(c_0_140,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(t_a,tc_bool)),X2),v_x) = hAPP(X2,v_x)
| ~ hBOOL(hAPP(X1,v_x)) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_141,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_133,c_0_134]) ).
cnf(c_0_142,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_bool)
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_83]),c_0_78]) ).
cnf(c_0_143,plain,
hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2))),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_144,plain,
( X1 = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),tc_bool)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_145,plain,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(t_a,tc_bool)),X2),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(hAPP(X2,v_x)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_66]),c_0_141]) ).
cnf(c_0_146,plain,
hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_142,c_0_71]) ).
cnf(c_0_147,negated_conjecture,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
cls_conjecture_3 ).
cnf(c_0_148,plain,
hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2))),
inference(spm,[status(thm)],[c_0_98,c_0_143]) ).
cnf(c_0_149,plain,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X3,tc_bool),tc_bool)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_144,c_0_112]) ).
cnf(c_0_150,plain,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1,tc_fun(t_a,tc_bool)),hAPP(c_Set_Oinsert(v_x,X2),X3)),v_x) = 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_145,c_0_146]),c_0_146]),c_0_71])]) ).
cnf(c_0_151,negated_conjecture,
hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(spm,[status(thm)],[c_0_91,c_0_147]) ).
cnf(c_0_152,plain,
( hBOOL(c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),tc_bool))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_153,plain,
( hAPP(X1,v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_in(v_x,X1,t_a)) ),
inference(spm,[status(thm)],[c_0_150,c_0_69]) ).
cnf(c_0_154,negated_conjecture,
hAPP(v_F(v_P),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),tc_bool),
inference(spm,[status(thm)],[c_0_144,c_0_151]) ).
cnf(c_0_155,plain,
hBOOL(c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),tc_bool)),
inference(spm,[status(thm)],[c_0_152,c_0_137]) ).
cnf(c_0_156,plain,
( hAPP(X1,v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(hAPP(X1,v_x)) ),
inference(spm,[status(thm)],[c_0_91,c_0_153]) ).
cnf(c_0_157,negated_conjecture,
hBOOL(hAPP(v_F(v_P),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(v_F(v_P),X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_154]),c_0_155])]) ).
cnf(c_0_158,plain,
( X1 = X2
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_127,c_0_102]) ).
cnf(c_0_159,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_156,c_0_78]) ).
cnf(c_0_160,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_161,negated_conjecture,
hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(v_F(v_P),X1),X2),v_F(v_P)) = v_F(v_P),
inference(spm,[status(thm)],[c_0_103,c_0_157]) ).
cnf(c_0_162,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| X1 = X2
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_163,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
cls_emptyE_0 ).
cnf(c_0_164,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_165,negated_conjecture,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != v_F(v_P),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_166,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| X2 = c_Orderings_Obot__class_Obot(tc_bool)
| X2 = X1 ),
inference(spm,[status(thm)],[c_0_162,c_0_159]) ).
cnf(c_0_167,plain,
c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(spm,[status(thm)],[c_0_163,c_0_164]) ).
cnf(c_0_168,negated_conjecture,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool)
| v_F(v_P) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166])]) ).
cnf(c_0_169,negated_conjecture,
c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_2 ).
cnf(c_0_170,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_171,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_172,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_6 ).
cnf(c_0_173,negated_conjecture,
( v_F(v_P) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),X1) ),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_174,negated_conjecture,
c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),hAPP(v_P,X2),tc_Arrow__Order__Mirabelle_Oalt),
inference(spm,[status(thm)],[c_0_169,c_0_80]) ).
cnf(c_0_175,negated_conjecture,
c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_0 ).
cnf(c_0_176,negated_conjecture,
c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_1 ).
cnf(c_0_177,axiom,
( c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I1_J_0 ).
cnf(c_0_178,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_170,c_0_171]) ).
cnf(c_0_179,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_180,negated_conjecture,
( c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),tc_Arrow__Order__Mirabelle_Oalt)
| c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_174]),c_0_175]),c_0_176])]) ).
cnf(c_0_181,plain,
c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X2),X1,tc_bool),
inference(spm,[status(thm)],[c_0_177,c_0_108]) ).
cnf(c_0_182,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1),tc_bool),X4) = X4,
inference(spm,[status(thm)],[c_0_178,c_0_146]) ).
cnf(c_0_183,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_Set_Oinsert(X3,X2),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X4)
| hBOOL(c_in(X3,X1,X2)) ),
cls_Int__insert__right_1 ).
cnf(c_0_184,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_179,c_0_80]) ).
cnf(c_0_185,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_186,axiom,
hBOOL(c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))),
cls_rtrancl_Ortrancl__refl_0 ).
cnf(c_0_187,negated_conjecture,
c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_bool),tc_Arrow__Order__Mirabelle_Oalt),
inference(ef,[status(thm)],[c_0_180]) ).
cnf(c_0_188,plain,
( X1 = X2
| hBOOL(X2)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_159,c_0_159]) ).
cnf(c_0_189,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_141]),c_0_67]) ).
cnf(c_0_190,plain,
c_lessequals(X1,hAPP(hAPP(c_Set_Oinsert(X2,X3),X4),X2),tc_bool),
inference(spm,[status(thm)],[c_0_181,c_0_182]) ).
cnf(c_0_191,plain,
( hAPP(c_Set_Oinsert(X1,X2),X3) = X3
| hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_184]),c_0_184]) ).
cnf(c_0_192,plain,
~ c_Relation_Oirrefl(c_Transitive__Closure_Ortrancl(X1,X2),X2),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_193,negated_conjecture,
( c_Relation_Oirrefl(X1,tc_Arrow__Order__Mirabelle_Oalt)
| hBOOL(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_189]) ).
cnf(c_0_194,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1) ),
cls_le__infE_0 ).
cnf(c_0_195,plain,
( hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3))
| c_lessequals(X4,hAPP(X5,X1),tc_bool) ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_196,negated_conjecture,
hBOOL(c_Transitive__Closure_Ortrancl(X1,tc_Arrow__Order__Mirabelle_Oalt)),
inference(spm,[status(thm)],[c_0_192,c_0_193]) ).
cnf(c_0_197,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__bot__right_0 ).
cnf(c_0_198,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__inf_0 ).
cnf(c_0_199,plain,
( hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3))
| c_lessequals(X4,X5,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_122])]) ).
cnf(c_0_200,negated_conjecture,
( X1 = c_Transitive__Closure_Ortrancl(X2,tc_Arrow__Order__Mirabelle_Oalt)
| X1 = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_162,c_0_196]) ).
cnf(c_0_201,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_197,c_0_171]) ).
cnf(c_0_202,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X2) = X1
| hBOOL(c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X5)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_199]),c_0_122])]) ).
cnf(c_0_203,negated_conjecture,
hAPP(v_P,X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_200]),c_0_192]) ).
cnf(c_0_204,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_in(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X4)) ),
inference(spm,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_205,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ hBOOL(hAPP(X1,c_Pair(X3,X3,X2,X2))) ),
inference(spm,[status(thm)],[c_0_185,c_0_97]) ).
cnf(c_0_206,plain,
~ hBOOL(hAPP(v_P,tc_bool)),
inference(rw,[status(thm)],[c_0_189,c_0_203]) ).
cnf(c_0_207,negated_conjecture,
hAPP(v_P,X1) = hAPP(v_P,X2),
inference(spm,[status(thm)],[c_0_203,c_0_203]) ).
cnf(c_0_208,axiom,
( hBOOL(c_in(X1,c_Relation_ODomain(X2,X3,X4),X3))
| ~ hBOOL(c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4))) ),
cls_Domain__iff_1 ).
cnf(c_0_209,plain,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_204]),c_0_189]) ).
cnf(c_0_210,plain,
~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2),
inference(spm,[status(thm)],[c_0_205,c_0_75]) ).
cnf(c_0_211,negated_conjecture,
~ hBOOL(hAPP(v_P,X1)),
inference(spm,[status(thm)],[c_0_206,c_0_207]) ).
cnf(c_0_212,plain,
hBOOL(c_in(X1,c_Relation_ODomain(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X4),X3)),
inference(spm,[status(thm)],[c_0_208,c_0_209]) ).
cnf(c_0_213,negated_conjecture,
( c_Transitive__Closure_Ortrancl(X1,tc_Arrow__Order__Mirabelle_Oalt) = X2
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_158,c_0_196]) ).
cnf(c_0_214,negated_conjecture,
hBOOL(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),
inference(spm,[status(thm)],[c_0_210,c_0_193]) ).
cnf(c_0_215,axiom,
( c_Transitive__Closure_Otrancl(X1,X2) = X1
| ~ c_Relation_Otrans(X1,X2) ),
cls_trancl__id_0 ).
cnf(c_0_216,axiom,
c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),
cls_trancl__unfold__left_0 ).
cnf(c_0_217,axiom,
c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_OId(X2)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
cls_rtrancl__reflcl_0 ).
cnf(c_0_218,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2) = X2,
cls_Un__empty__left_0 ).
cnf(c_0_219,negated_conjecture,
( X1 = hAPP(v_P,X2)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_211,c_0_188]) ).
cnf(c_0_220,plain,
c_Relation_ODomain(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X3) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_76,c_0_212]) ).
cnf(c_0_221,negated_conjecture,
c_Transitive__Closure_Ortrancl(X1,tc_Arrow__Order__Mirabelle_Oalt) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_213,c_0_214]) ).
cnf(c_0_222,plain,
( c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = X1
| ~ c_Relation_Otrans(X1,X2) ),
inference(rw,[status(thm)],[c_0_215,c_0_216]) ).
cnf(c_0_223,axiom,
c_Relation_Otrans(c_Relation_OId(X1),X1),
cls_trans__Id_0 ).
cnf(c_0_224,axiom,
c_Relation_Orel__comp(c_Relation_OId(X1),X2,X1,X1,X3) = X2,
cls_Id__O__R_0 ).
cnf(c_0_225,plain,
c_Transitive__Closure_Ortrancl(c_Relation_OId(X1),X1) = c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(spm,[status(thm)],[c_0_217,c_0_218]) ).
cnf(c_0_226,negated_conjecture,
hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(tc_bool,tc_Arrow__Order__Mirabelle_Oalt),X2)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_219]),c_0_220]),c_0_221]),c_0_211]) ).
cnf(c_0_227,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_UNIV__not__empty_0 ).
cnf(c_0_228,axiom,
( X1 = X2
| ~ hBOOL(c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId(X3),tc_prod(X3,X3))) ),
cls_pair__in__Id__conv_0 ).
cnf(c_0_229,plain,
c_Relation_OId(X1) = c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_223]),c_0_224]),c_0_225]) ).
cnf(c_0_230,negated_conjecture,
hBOOL(hAPP(c_Transitive__Closure_Ortrancl(tc_bool,tc_Arrow__Order__Mirabelle_Oalt),X1)),
inference(spm,[status(thm)],[c_0_91,c_0_226]) ).
cnf(c_0_231,negated_conjecture,
c_Transitive__Closure_Ortrancl(X1,tc_Arrow__Order__Mirabelle_Oalt) = c_Transitive__Closure_Ortrancl(X2,tc_Arrow__Order__Mirabelle_Oalt),
inference(spm,[status(thm)],[c_0_213,c_0_196]) ).
cnf(c_0_232,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_227,c_0_80]) ).
cnf(c_0_233,plain,
( X1 = X2
| ~ hBOOL(hAPP(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)),X3),c_Pair(X1,X2,X3,X3))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_97]),c_0_229]) ).
cnf(c_0_234,negated_conjecture,
hBOOL(hAPP(c_Transitive__Closure_Ortrancl(X1,tc_Arrow__Order__Mirabelle_Oalt),X2)),
inference(spm,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_235,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Transitive__Closure_Ortrancl(tc_bool,tc_Arrow__Order__Mirabelle_Oalt),
inference(rw,[status(thm)],[c_0_232,c_0_221]) ).
cnf(c_0_236,negated_conjecture,
X1 = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_231]),c_0_234])]) ).
cnf(c_0_237,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_235,c_0_236]),c_0_236])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT020-1 : 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
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 16:13:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.59 start to proof: theBenchmark
% 78.67/78.87 % Version : CSE_E---1.5
% 78.67/78.87 % Problem : theBenchmark.p
% 78.67/78.87 % Proof found
% 78.67/78.87 % SZS status Theorem for theBenchmark.p
% 78.67/78.87 % SZS output start Proof
% See solution above
% 78.67/78.89 % Total time : 78.087000 s
% 78.67/78.89 % SZS output end Proof
% 78.67/78.89 % Total time : 78.116000 s
%------------------------------------------------------------------------------