TSTP Solution File: SCT023-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SCT023-1 : 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 : n021.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 0.63s 0.97s
% Output   : CNFRefutation 0.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  107
% Syntax   : Number of formulae    :  134 (  17 unt;  93 typ;   0 def)
%            Number of atoms       :   77 (   8 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   70 (  34   ~;  36   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  222 (  84   >; 138   *;   0   +;   0  <<)
%            Number of predicates  :   33 (  31 usr;   1 prp; 0-6 aty)
%            Number of functors    :   62 (  62 usr;   9 con; 0-5 aty)
%            Number of variables   :   81 (   8 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    class_Lattices_Olattice: $i > $o ).

tff(decl_23,type,
    c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).

tff(decl_24,type,
    class_Lattices_Oupper__semilattice: $i > $o ).

tff(decl_25,type,
    tc_bool: $i ).

tff(decl_26,type,
    tc_fun: ( $i * $i ) > $i ).

tff(decl_27,type,
    c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).

tff(decl_28,type,
    c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

tff(decl_29,type,
    c_lessequals: ( $i * $i * $i ) > $o ).

tff(decl_30,type,
    c_Orderings_Obot__class_Obot: $i > $i ).

tff(decl_31,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

tff(decl_32,type,
    c_Set_Oinsert: ( $i * $i * $i ) > $i ).

tff(decl_33,type,
    c_COMBK: ( $i * $i * $i ) > $i ).

tff(decl_34,type,
    hAPP: ( $i * $i ) > $i ).

tff(decl_35,type,
    c_Relation_OImage: ( $i * $i * $i * $i ) > $i ).

tff(decl_36,type,
    tc_prod: ( $i * $i ) > $i ).

tff(decl_37,type,
    class_Lattices_Odistrib__lattice: $i > $o ).

tff(decl_38,type,
    c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).

tff(decl_39,type,
    c_Relation_ODomain: ( $i * $i * $i ) > $i ).

tff(decl_40,type,
    c_in: ( $i * $i * $i ) > $o ).

tff(decl_41,type,
    c_Product__Type_OSigma: ( $i * $i * $i * $i ) > $i ).

tff(decl_42,type,
    c_Relation_ORange: ( $i * $i * $i ) > $i ).

tff(decl_43,type,
    c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).

tff(decl_44,type,
    class_Orderings_Obot: $i > $o ).

tff(decl_45,type,
    c_Relation_Osym: ( $i * $i ) > $o ).

tff(decl_46,type,
    class_Lattices_Obounded__lattice: $i > $o ).

tff(decl_47,type,
    hBOOL: $i > $o ).

tff(decl_48,type,
    c_Wellfounded_Owf: ( $i * $i ) > $o ).

tff(decl_49,type,
    c_Relation_Orefl__on: ( $i * $i * $i ) > $o ).

tff(decl_50,type,
    class_Lattices_Olower__semilattice: $i > $o ).

tff(decl_51,type,
    c_Pair: ( $i * $i * $i * $i ) > $i ).

tff(decl_52,type,
    c_Wellfounded_Oacyclic: ( $i * $i ) > $o ).

tff(decl_53,type,
    c_Relation_Oconverse: ( $i * $i * $i ) > $i ).

tff(decl_54,type,
    c_Relation_Ototal__on: ( $i * $i * $i ) > $o ).

tff(decl_55,type,
    c_Order__Relation_Ostrict__linear__order__on: ( $i * $i * $i ) > $o ).

tff(decl_56,type,
    c_Relation_Orel__comp: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_57,type,
    c_Relation_Otrans: ( $i * $i ) > $o ).

tff(decl_58,type,
    c_Relation_OId: $i > $i ).

tff(decl_59,type,
    c_Relation_Oirrefl: ( $i * $i ) > $o ).

tff(decl_60,type,
    c_Transitive__Closure_Otrancl: ( $i * $i ) > $i ).

tff(decl_61,type,
    c_Equiv__Relations_Oequiv: ( $i * $i * $i ) > $o ).

tff(decl_62,type,
    c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_63,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

tff(decl_64,type,
    c_ATP__Linkup_Osko__Relation__XImageE__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_65,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1: ( $i * $i * $i ) > $i ).

tff(decl_66,type,
    c_Wellfounded_Oacc: ( $i * $i ) > $i ).

tff(decl_67,type,
    c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    c_Relation_Oantisym: ( $i * $i ) > $o ).

tff(decl_69,type,
    c_Relation_OId__on: ( $i * $i ) > $i ).

tff(decl_70,type,
    v_r: $i ).

tff(decl_71,type,
    t_a: $i ).

tff(decl_72,type,
    t_b: $i ).

tff(decl_73,type,
    c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1: ( $i * $i ) > $i ).

tff(decl_74,type,
    c_Relation_Osingle__valued: ( $i * $i * $i ) > $o ).

tff(decl_75,type,
    c_Nitpick_Orefl_H: ( $i * $i ) > $o ).

tff(decl_76,type,
    c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1: ( $i * $i ) > $i ).

tff(decl_77,type,
    c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_78,type,
    c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_79,type,
    class_Orderings_Olinorder: $i > $o ).

tff(decl_80,type,
    class_Orderings_Opreorder: $i > $o ).

tff(decl_81,type,
    class_Orderings_Oorder: $i > $o ).

tff(decl_82,type,
    class_HOL_Oord: $i > $o ).

tff(decl_83,type,
    c_Relation_Oinv__image: ( $i * $i * $i * $i ) > $i ).

tff(decl_84,type,
    c_split: ( $i * $i * $i * $i ) > $i ).

tff(decl_85,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1: ( $i * $i * $i ) > $i ).

tff(decl_86,type,
    v_sko__Wellfounded__Xacc__Xinducts__1: ( $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__Wellfounded__Xwf__eq__minimal__1__1: ( $i * $i * $i ) > $i ).

tff(decl_89,type,
    v_sko__Wellfounded__Xacc__Xinduct__1: ( $i * $i ) > $i ).

tff(decl_90,type,
    c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1: ( $i * $i * $i ) > $i ).

tff(decl_91,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1: ( $i * $i * $i ) > $i ).

tff(decl_92,type,
    c_Equiv__Relations_Ocongruent: ( $i * $i * $i * $i ) > $o ).

tff(decl_93,type,
    c_Equiv__Relations_Ocongruent2: ( $i * $i * $i * $i * $i * $i ) > $o ).

tff(decl_94,type,
    c_ATP__Linkup_Osko__Relation__XRangeE__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_95,type,
    c_ATP__Linkup_Osko__Relation__XDomainE__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_96,type,
    c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_97,type,
    c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_98,type,
    c_ATP__Linkup_Osko__Relation__XtransI__1__1: ( $i * $i ) > $i ).

tff(decl_99,type,
    c_ATP__Linkup_Osko__Relation__XtransI__1__3: ( $i * $i ) > $i ).

tff(decl_100,type,
    c_ATP__Linkup_Osko__Relation__XtransI__1__2: ( $i * $i ) > $i ).

tff(decl_101,type,
    c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1: ( $i * $i ) > $i ).

tff(decl_102,type,
    c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2: ( $i * $i ) > $i ).

tff(decl_103,type,
    c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3: ( $i * $i ) > $i ).

tff(decl_104,type,
    c_Recdef_Ocut: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_105,type,
    c_FunDef_Oin__rel: ( $i * $i * $i * $i * $i ) > $o ).

tff(decl_106,type,
    tc_Arrow__Order__Mirabelle_Oalt: $i ).

tff(decl_107,type,
    c_Arrow__Order__Mirabelle_Omktop: ( $i * $i ) > $i ).

tff(decl_108,type,
    c_Arrow__Order__Mirabelle_Omkbot: ( $i * $i ) > $i ).

tff(decl_109,type,
    v_P: $i ).

tff(decl_110,type,
    v_a: $i ).

tff(decl_111,type,
    v_b: $i ).

tff(decl_112,type,
    v_F: $i > $i ).

tff(decl_113,type,
    v_i: $i ).

tff(decl_114,type,
    c_fequal: ( $i * $i * $i ) > $o ).

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

cnf(cls_conjecture_2,negated_conjecture,
    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_2) ).

cnf(cls_mem__def_1,axiom,
    ( c_in(X1,X2,X3)
    | ~ hBOOL(hAPP(X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).

cnf(cls_trans__def_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_Relation_Otrans(X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__def_0) ).

cnf(cls_conjecture_3,negated_conjecture,
    c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(cls_conjecture_4,negated_conjecture,
    ~ c_in(c_Pair(X1,X1,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_irrefl__def_1,axiom,
    ( c_Relation_Oirrefl(X1,X2)
    | 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/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_1) ).

cnf(cls_conjecture_8,negated_conjecture,
    ( 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))
    | X1 = X2
    | ~ 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)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).

cnf(cls_rev__ImageI_0,axiom,
    ( c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
    | ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
    | ~ c_in(X6,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).

cnf(cls_irrefl__def_0,axiom,
    ( ~ 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(cls_Image__singleton__iff_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_in(X2,c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X4),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).

cnf(cls_conjecture_6,negated_conjecture,
    ( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | X2 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).

cnf(cls_conjecture_5,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),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).

cnf(cls_insert__iff_1,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).

cnf(c_0_14,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ c_in(X2,X1,X3) ),
    cls_mem__def_0 ).

cnf(c_0_15,negated_conjecture,
    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_2 ).

cnf(c_0_16,axiom,
    ( c_in(X1,X2,X3)
    | ~ hBOOL(hAPP(X2,X1)) ),
    cls_mem__def_1 ).

cnf(c_0_17,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_14,c_0_15]) ).

cnf(c_0_18,axiom,
    ( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3))
    | ~ c_Relation_Otrans(X4,X3) ),
    cls_trans__def_0 ).

cnf(c_0_19,negated_conjecture,
    c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),X1),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,negated_conjecture,
    c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
    cls_conjecture_3 ).

cnf(c_0_21,negated_conjecture,
    ~ c_in(c_Pair(X1,X1,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_22,axiom,
    ( c_Relation_Oirrefl(X1,X2)
    | 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_23,negated_conjecture,
    ( 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))
    | X1 = X2
    | ~ 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)) ),
    cls_conjecture_8 ).

cnf(c_0_24,axiom,
    ( c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
    | ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
    | ~ c_in(X6,X3,X4) ),
    cls_rev__ImageI_0 ).

cnf(c_0_25,axiom,
    ( ~ 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_26,negated_conjecture,
    ( c_in(c_Pair(X1,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))
    | ~ c_in(c_Pair(X1,v_a,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)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).

cnf(c_0_27,negated_conjecture,
    c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_28,negated_conjecture,
    ( X1 = X2
    | hBOOL(hAPP(v_F(v_P),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ 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(spm,[status(thm)],[c_0_14,c_0_23]) ).

cnf(c_0_29,axiom,
    ( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_in(X2,c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X4),X4) ),
    cls_Image__singleton__iff_0 ).

cnf(c_0_30,negated_conjecture,
    ( c_in(v_b,c_Relation_OImage(v_F(v_P),X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_in(v_a,X1,tc_Arrow__Order__Mirabelle_Oalt) ),
    inference(spm,[status(thm)],[c_0_24,c_0_19]) ).

cnf(c_0_31,negated_conjecture,
    ~ c_in(c_Pair(v_b,v_a,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)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).

cnf(c_0_32,negated_conjecture,
    ( X1 = X2
    | c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),X3)
    | ~ 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(spm,[status(thm)],[c_0_16,c_0_28]) ).

cnf(c_0_33,negated_conjecture,
    ( c_in(c_Pair(X1,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))
    | ~ c_in(v_a,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_34,negated_conjecture,
    ( v_b = v_a
    | ~ c_in(c_Pair(v_b,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_31,c_0_32]) ).

cnf(c_0_35,negated_conjecture,
    ( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | X2 = X1 ),
    cls_conjecture_6 ).

cnf(c_0_36,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),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
    cls_conjecture_5 ).

cnf(c_0_37,negated_conjecture,
    ~ c_in(v_a,c_Set_Oinsert(v_b,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_33]),c_0_27])]) ).

cnf(c_0_38,negated_conjecture,
    v_b = v_a,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_39,axiom,
    c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
    cls_insert__iff_1 ).

cnf(c_0_40,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SCT023-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Aug 24 15:00:25 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.21/0.62  start to proof: theBenchmark
% 0.63/0.97  % Version  : CSE_E---1.5
% 0.63/0.97  % Problem  : theBenchmark.p
% 0.63/0.97  % Proof found
% 0.63/0.97  % SZS status Theorem for theBenchmark.p
% 0.63/0.97  % SZS output start Proof
% See solution above
% 0.63/0.98  % Total time : 0.329000 s
% 0.63/0.98  % SZS output end Proof
% 0.63/0.98  % Total time : 0.348000 s
%------------------------------------------------------------------------------