TSTP Solution File: SWV879-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV879-1 : 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 : n032.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 21:48:29 EDT 2023

% Result   : Unsatisfiable 0.85s 1.00s
% Output   : CNFRefutation 0.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :  112
% Syntax   : Number of formulae    :  135 (  21 unt;  99 typ;   0 def)
%            Number of atoms       :   53 (  11 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   40 (  23   ~;  17   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  178 (  90   >;  88   *;   0   +;   0  <<)
%            Number of predicates  :   49 (  47 usr;   1 prp; 0-9 aty)
%            Number of functors    :   52 (  52 usr;   9 con; 0-5 aty)
%            Number of variables   :   65 (  13 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    class_Orderings_Oorder: $i > $o ).

tff(decl_26,type,
    tc_bool: $i ).

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

tff(decl_28,type,
    c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).

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

tff(decl_30,type,
    hAPP: ( $i * $i ) > $i ).

tff(decl_31,type,
    c_SetInterval_Oord__class_OatLeastAtMost: ( $i * $i * $i ) > $i ).

tff(decl_32,type,
    c_Orderings_Obot__class_Obot: $i > $i ).

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

tff(decl_34,type,
    c_Orderings_Otop__class_Otop: $i > $i ).

tff(decl_35,type,
    class_Lattices_Obounded__lattice: $i > $o ).

tff(decl_36,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

tff(decl_37,type,
    c_HOL_Otimes__class_Otimes: $i > $i ).

tff(decl_38,type,
    c_Suc: $i > $i ).

tff(decl_39,type,
    tc_nat: $i ).

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

tff(decl_41,type,
    class_Int_Onumber__ring: $i > $o ).

tff(decl_42,type,
    c_HOL_Oplus__class_Oplus: $i > $i ).

tff(decl_43,type,
    class_Orderings_Olinorder: $i > $o ).

tff(decl_44,type,
    c_Orderings_Oord__class_Omin: $i > $i ).

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

tff(decl_46,type,
    c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).

tff(decl_47,type,
    c_Orderings_Oord__class_Omax: $i > $i ).

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

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

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

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

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

tff(decl_53,type,
    class_Ring__and__Field_Opordered__ring: $i > $o ).

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

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

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

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

tff(decl_58,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

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

tff(decl_60,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

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

tff(decl_62,type,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).

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

tff(decl_64,type,
    class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).

tff(decl_65,type,
    class_Lattices_Odistrib__lattice: $i > $o ).

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

tff(decl_67,type,
    t_a: $i ).

tff(decl_68,type,
    v_x: $i ).

tff(decl_69,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

tff(decl_70,type,
    class_OrderedGroup_Olordered__ab__group__add: $i > $o ).

tff(decl_71,type,
    c_Finite__Set_Ocard: ( $i * $i ) > $i ).

tff(decl_72,type,
    class_Ring__and__Field_Oring: $i > $o ).

tff(decl_73,type,
    class_OrderedGroup_Ogroup__add: $i > $o ).

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

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

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

tff(decl_77,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

tff(decl_78,type,
    class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).

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

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

tff(decl_81,type,
    c_Set_Oinsert: ( $i * $i * $i ) > $i ).

tff(decl_82,type,
    c_in: ( $i * $i * $i ) > $i ).

tff(decl_83,type,
    c_Finite__Set_Ofold1: ( $i * $i ) > $i ).

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

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

tff(decl_86,type,
    c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).

tff(decl_87,type,
    c_Fun_Obij: ( $i * $i * $i ) > $o ).

tff(decl_88,type,
    c_Set_Ovimage: ( $i * $i * $i * $i ) > $i ).

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

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

tff(decl_91,type,
    c_Finite__Set_Olinorder__class_OMax: $i > $i ).

tff(decl_92,type,
    c_Finite__Set_Olinorder__class_OMin: $i > $i ).

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

tff(decl_94,type,
    class_Ring__and__Field_Osemiring: $i > $o ).

tff(decl_95,type,
    class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).

tff(decl_96,type,
    class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).

tff(decl_97,type,
    class_Ring__and__Field_Oordered__ring__strict: $i > $o ).

tff(decl_98,type,
    c_Finite__Set_Ofold1Set: ( $i * $i * $i ) > $i ).

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

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

tff(decl_101,type,
    class_HOL_Ominus: $i > $o ).

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

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

tff(decl_104,type,
    class_Finite__Set_Ofinite_Ofinite: $i > $o ).

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

tff(decl_106,type,
    c_ATP__Linkup_Osko__Set__Ximage__cong__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_107,type,
    v_P: $i ).

tff(decl_108,type,
    c_ATP__Linkup_Osko__Set__XimageE__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_109,type,
    c_ATP__Linkup_Osko__Set__Ximage__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_110,type,
    class_Orderings_Otop: $i > $o ).

tff(decl_111,type,
    c_fequal: ( $i * $i ) > $i ).

tff(decl_112,type,
    c_Nitpick_Osko__Nitpick__XEx1__def__1__3: ( $i * $i ) > $i ).

tff(decl_113,type,
    c_Set_Ocontents: ( $i * $i ) > $i ).

tff(decl_114,type,
    v_mgt: $i > $i ).

tff(decl_115,type,
    v_mgt__call: $i ).

tff(decl_116,type,
    v_U: $i ).

tff(decl_117,type,
    v_sko__local__Xassms__3__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_118,type,
    v_wt: $i > $o ).

tff(decl_119,type,
    tc_Com_Opname: $i ).

tff(decl_120,type,
    v_G: $i ).

cnf(cls_conjecture_3,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(cls_conjecture_1,negated_conjecture,
    v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_insert__absorb_0,axiom,
    ( c_Set_Oinsert(X1,X2,X3) = X2
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

cnf(cls_conjecture_2,negated_conjecture,
    hBOOL(c_in(v_x,v_U,tc_Com_Opname)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(cls_assms_I1_J_0,axiom,
    ( hBOOL(hAPP(hAPP(v_P,X1),X2))
    | ~ c_lessequals(X2,X1,tc_fun(t_a,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_assms_I1_J_0) ).

cnf(cls_insert__image_0,axiom,
    ( c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) = c_Set_Oimage(X1,X3,X4,X5)
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).

cnf(cls_insert__subset_0,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).

cnf(cls_insert__subset_2,axiom,
    ( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ hBOOL(c_in(X1,X4,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).

cnf(cls_empty__subsetI_0,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

cnf(cls_CollectI_0,axiom,
    ( hBOOL(c_in(X1,c_Collect(X2,X3),X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectI_0) ).

cnf(cls_Collect__def_0,axiom,
    c_Collect(X1,X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).

cnf(cls_equalityE_0,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).

cnf(cls_insert__code_1,axiom,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).

cnf(c_0_13,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
    cls_conjecture_3 ).

cnf(c_0_14,negated_conjecture,
    v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
    cls_conjecture_1 ).

cnf(c_0_15,axiom,
    ( c_Set_Oinsert(X1,X2,X3) = X2
    | ~ hBOOL(c_in(X1,X2,X3)) ),
    cls_insert__absorb_0 ).

cnf(c_0_16,negated_conjecture,
    hBOOL(c_in(v_x,v_U,tc_Com_Opname)),
    cls_conjecture_2 ).

cnf(c_0_17,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,axiom,
    ( hBOOL(hAPP(hAPP(v_P,X1),X2))
    | ~ c_lessequals(X2,X1,tc_fun(t_a,tc_bool)) ),
    cls_assms_I1_J_0 ).

cnf(c_0_19,axiom,
    ( c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) = c_Set_Oimage(X1,X3,X4,X5)
    | ~ hBOOL(c_in(X2,X3,X4)) ),
    cls_insert__image_0 ).

cnf(c_0_20,axiom,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
    cls_insert__subset_0 ).

cnf(c_0_21,negated_conjecture,
    c_Set_Oinsert(v_x,v_U,tc_Com_Opname) = v_U,
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_22,negated_conjecture,
    ~ c_lessequals(c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),v_G,tc_fun(t_a,tc_bool)),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,axiom,
    ( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
    | ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
    | ~ hBOOL(c_in(X1,X4,X3)) ),
    cls_insert__subset_2 ).

cnf(c_0_24,axiom,
    c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
    cls_empty__subsetI_0 ).

cnf(c_0_25,axiom,
    ( hBOOL(c_in(X1,c_Collect(X2,X3),X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    cls_CollectI_0 ).

cnf(c_0_26,axiom,
    c_Collect(X1,X2) = X1,
    cls_Collect__def_0 ).

cnf(c_0_27,negated_conjecture,
    ( c_Set_Oinsert(hAPP(v_mgt__call,X1),v_G,t_a) = v_G
    | ~ hBOOL(c_in(X1,v_U,tc_Com_Opname)) ),
    inference(spm,[status(thm)],[c_0_19,c_0_14]) ).

cnf(c_0_28,negated_conjecture,
    ( hBOOL(c_in(v_x,X1,tc_Com_Opname))
    | ~ c_lessequals(v_U,X1,tc_fun(tc_Com_Opname,tc_bool)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_29,axiom,
    c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    cls_equalityE_0 ).

cnf(c_0_30,negated_conjecture,
    ~ hBOOL(c_in(hAPP(v_mgt__call,v_x),v_G,t_a)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_31,plain,
    ( hBOOL(c_in(X1,X2,X3))
    | ~ hBOOL(hAPP(X2,X1)) ),
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_32,axiom,
    hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
    cls_insert__code_1 ).

cnf(c_0_33,negated_conjecture,
    c_Set_Oinsert(hAPP(v_mgt__call,v_x),v_G,t_a) = v_G,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).

cnf(c_0_34,negated_conjecture,
    ~ hBOOL(hAPP(v_G,hAPP(v_mgt__call,v_x))),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem    : SWV879-1 : TPTP v8.1.2. Released v4.1.0.
% 0.05/0.10  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Tue Aug 29 05:07:01 EDT 2023
% 0.09/0.29  % CPUTime  : 
% 0.13/0.47  start to proof: theBenchmark
% 0.85/1.00  % Version  : CSE_E---1.5
% 0.85/1.00  % Problem  : theBenchmark.p
% 0.85/1.00  % Proof found
% 0.85/1.00  % SZS status Theorem for theBenchmark.p
% 0.85/1.00  % SZS output start Proof
% See solution above
% 0.85/1.01  % Total time : 0.500000 s
% 0.85/1.01  % SZS output end Proof
% 0.85/1.01  % Total time : 0.526000 s
%------------------------------------------------------------------------------