TSTP Solution File: SCT024-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SCT024-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n020.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 14:10:47 EDT 2023

% Result   : Unsatisfiable 28.81s 29.07s
% Output   : CNFRefutation 28.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :  152
% Syntax   : Number of formulae    :  203 (  37 unt; 126 typ;   0 def)
%            Number of atoms       :  127 (  32 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  101 (  51   ~;  50   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    5 (   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   :  134 (  46 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_i: $i ).

tff(decl_145,type,
    v_F: $i > $i ).

tff(decl_146,type,
    v_Pa: $i > $i ).

tff(decl_147,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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).

cnf(clsarity_bool__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

cnf(cls_COMBK__def_0,axiom,
    hAPP(c_COMBK(X1,X2,X3),X4) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

cnf(cls_top__fun__eq_0,axiom,
    ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Orderings_Otop(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).

cnf(clsarity_bool__Orderings_Otop,axiom,
    class_Orderings_Otop(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

cnf(cls_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/sandbox2/benchmark/theBenchmark.p',cls_sup__top__left_0) ).

cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

cnf(cls_top1I_0,axiom,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).

cnf(cls_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

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/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).

cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
    class_Lattices_Oupper__semilattice(tc_bool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

cnf(cls_mem__def_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).

cnf(cls_conjecture_3,negated_conjecture,
    hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(cls_conjecture_8,negated_conjecture,
    ( hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | X1 = X2
    | ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Oirrefl(hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Otrans(hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
    file('/export/starexec/sandbox2/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_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(cls_conjecture_1,negated_conjecture,
    c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_in__rel__def_1,axiom,
    ( c_FunDef_Oin__rel(X1,X2,X3,X4,X5)
    | ~ hBOOL(c_in(c_Pair(X2,X3,X4,X5),X1,tc_prod(X4,X5))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rel__def_1) ).

cnf(cls_conjecture_4,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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).

cnf(cls_in__rel__def_0,axiom,
    ( hBOOL(c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)))
    | ~ c_FunDef_Oin__rel(X5,X1,X2,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rel__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/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_0) ).

cnf(c_0_26,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_27,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_28,axiom,
    class_Lattices_Olattice(tc_bool),
    clsarity_bool__Lattices_Olattice ).

cnf(c_0_29,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_26,c_0_27]),c_0_28])]) ).

cnf(c_0_30,axiom,
    hAPP(c_COMBK(X1,X2,X3),X4) = X1,
    cls_COMBK__def_0 ).

cnf(c_0_31,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_32,axiom,
    class_Orderings_Otop(tc_bool),
    clsarity_bool__Orderings_Otop ).

cnf(c_0_33,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),tc_bool),X1)) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_34,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_35,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    clsarity_bool__Lattices_Obounded__lattice ).

cnf(c_0_36,axiom,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
    cls_top1I_0 ).

cnf(c_0_37,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_31,c_0_32]) ).

cnf(c_0_38,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_bool),X1)) ),
    inference(spm,[status(thm)],[c_0_33,c_0_30]) ).

cnf(c_0_39,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_40,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    cls_mem__def_1 ).

cnf(c_0_41,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_34,c_0_35]) ).

cnf(c_0_42,plain,
    hBOOL(c_Orderings_Otop__class_Otop(tc_bool)),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_43,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_38,c_0_39]),c_0_28])]) ).

cnf(c_0_44,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_45,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_40,c_0_41]),c_0_42])]) ).

cnf(c_0_46,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_47,plain,
    ( hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),X3))
    | ~ hBOOL(X2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_43]) ).

cnf(c_0_48,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_49,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_44,c_0_45]) ).

cnf(c_0_50,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_46,c_0_35]) ).

cnf(c_0_51,axiom,
    ( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X2) = X2
    | ~ class_Lattices_Oupper__semilattice(X1) ),
    cls_sup__idem_0 ).

cnf(c_0_52,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_44,c_0_47]) ).

cnf(c_0_53,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_48,c_0_49]),c_0_50]),c_0_28])]) ).

cnf(c_0_54,axiom,
    class_Lattices_Oupper__semilattice(tc_bool),
    clsarity_bool__Lattices_Oupper__semilattice ).

cnf(c_0_55,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_51,c_0_52]),c_0_53]),c_0_54])]) ).

cnf(c_0_56,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(c_in(X2,X1,X3)) ),
    cls_mem__def_0 ).

cnf(c_0_57,negated_conjecture,
    hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    cls_conjecture_3 ).

cnf(c_0_58,plain,
    ( X1 = X2
    | ~ hBOOL(X2)
    | ~ hBOOL(X1) ),
    inference(spm,[status(thm)],[c_0_55,c_0_55]) ).

cnf(c_0_59,negated_conjecture,
    hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_60,negated_conjecture,
    ( hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | X1 = X2
    | ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Oirrefl(hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Otrans(hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt) ),
    cls_conjecture_8 ).

cnf(c_0_61,negated_conjecture,
    c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
    cls_conjecture_0 ).

cnf(c_0_62,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_63,negated_conjecture,
    c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
    cls_conjecture_1 ).

cnf(c_0_64,negated_conjecture,
    ( hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = X1
    | ~ hBOOL(X1) ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_65,negated_conjecture,
    hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),X1)),
    inference(spm,[status(thm)],[c_0_40,c_0_59]) ).

cnf(c_0_66,axiom,
    ( c_FunDef_Oin__rel(X1,X2,X3,X4,X5)
    | ~ hBOOL(c_in(c_Pair(X2,X3,X4,X5),X1,tc_prod(X4,X5))) ),
    cls_in__rel__def_1 ).

cnf(c_0_67,negated_conjecture,
    ( X1 = X2
    | hBOOL(c_in(c_Pair(X1,X2,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)))
    | ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_63])]) ).

cnf(c_0_68,negated_conjecture,
    c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),X1) = hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_69,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_4 ).

cnf(c_0_70,negated_conjecture,
    c_FunDef_Oin__rel(hAPP(v_P,v_i),v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),
    inference(spm,[status(thm)],[c_0_66,c_0_57]) ).

cnf(c_0_71,negated_conjecture,
    v_b = v_a,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_59])]),c_0_69]) ).

cnf(c_0_72,axiom,
    ( hBOOL(c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)))
    | ~ c_FunDef_Oin__rel(X5,X1,X2,X3,X4) ),
    cls_in__rel__def_0 ).

cnf(c_0_73,negated_conjecture,
    c_FunDef_Oin__rel(hAPP(v_P,v_i),v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),
    inference(rw,[status(thm)],[c_0_70,c_0_71]) ).

cnf(c_0_74,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_75,negated_conjecture,
    hBOOL(c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

cnf(c_0_76,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_63])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SCT024-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.11  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.31  % Computer : n020.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Thu Aug 24 16:39:00 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 0.15/0.56  start to proof: theBenchmark
% 28.81/29.07  % Version  : CSE_E---1.5
% 28.81/29.07  % Problem  : theBenchmark.p
% 28.81/29.07  % Proof found
% 28.81/29.07  % SZS status Theorem for theBenchmark.p
% 28.81/29.07  % SZS output start Proof
% See solution above
% 28.81/29.08  % Total time : 28.405000 s
% 28.81/29.08  % SZS output end Proof
% 28.81/29.08  % Total time : 28.427000 s
%------------------------------------------------------------------------------