TSTP Solution File: LAT291+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT291+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n012.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 06:00:40 EDT 2023

% Result   : Theorem 0.20s 0.78s
% Output   : CNFRefutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   89
% Syntax   : Number of formulae    :  118 (  13 unt;  82 typ;   0 def)
%            Number of atoms       :  126 (  21 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  142 (  52   ~;  38   |;  39   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   96 (  70   >;  26   *;   0   +;   0  <<)
%            Number of predicates  :   50 (  48 usr;   3 prp; 0-3 aty)
%            Number of functors    :   34 (  34 usr;  10 con; 0-4 aty)
%            Number of variables   :   28 (   0 sgn;  21   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    v3_struct_0: $i > $o ).

tff(decl_23,type,
    v10_lattices: $i > $o ).

tff(decl_24,type,
    v17_lattices: $i > $o ).

tff(decl_25,type,
    v3_realset2: $i > $o ).

tff(decl_26,type,
    l3_lattices: $i > $o ).

tff(decl_27,type,
    u1_struct_0: $i > $i ).

tff(decl_28,type,
    k7_lopclset: $i > $i ).

tff(decl_29,type,
    k1_zfmisc_1: $i > $i ).

tff(decl_30,type,
    k9_lopclset: $i > $i ).

tff(decl_31,type,
    k6_lattices: $i > $i ).

tff(decl_32,type,
    k8_funct_2: ( $i * $i * $i * $i ) > $i ).

tff(decl_33,type,
    r2_hidden: ( $i * $i ) > $o ).

tff(decl_34,type,
    v1_membered: $i > $o ).

tff(decl_35,type,
    m1_subset_1: ( $i * $i ) > $o ).

tff(decl_36,type,
    v1_xcmplx_0: $i > $o ).

tff(decl_37,type,
    v2_membered: $i > $o ).

tff(decl_38,type,
    v1_xreal_0: $i > $o ).

tff(decl_39,type,
    v3_membered: $i > $o ).

tff(decl_40,type,
    v1_rat_1: $i > $o ).

tff(decl_41,type,
    v4_membered: $i > $o ).

tff(decl_42,type,
    v1_int_1: $i > $o ).

tff(decl_43,type,
    v5_membered: $i > $o ).

tff(decl_44,type,
    v4_ordinal2: $i > $o ).

tff(decl_45,type,
    v1_xboole_0: $i > $o ).

tff(decl_46,type,
    v1_finset_1: $i > $o ).

tff(decl_47,type,
    v4_finsub_1: $i > $o ).

tff(decl_48,type,
    v1_finsub_1: $i > $o ).

tff(decl_49,type,
    v3_finsub_1: $i > $o ).

tff(decl_50,type,
    m1_relset_1: ( $i * $i * $i ) > $o ).

tff(decl_51,type,
    v1_funct_1: $i > $o ).

tff(decl_52,type,
    v1_partfun1: ( $i * $i * $i ) > $o ).

tff(decl_53,type,
    v1_funct_2: ( $i * $i * $i ) > $o ).

tff(decl_54,type,
    v4_lattices: $i > $o ).

tff(decl_55,type,
    v5_lattices: $i > $o ).

tff(decl_56,type,
    v6_lattices: $i > $o ).

tff(decl_57,type,
    v7_lattices: $i > $o ).

tff(decl_58,type,
    v8_lattices: $i > $o ).

tff(decl_59,type,
    v9_lattices: $i > $o ).

tff(decl_60,type,
    k2_zfmisc_1: ( $i * $i ) > $i ).

tff(decl_61,type,
    v1_relat_1: $i > $o ).

tff(decl_62,type,
    v13_lattices: $i > $o ).

tff(decl_63,type,
    v14_lattices: $i > $o ).

tff(decl_64,type,
    v15_lattices: $i > $o ).

tff(decl_65,type,
    v11_lattices: $i > $o ).

tff(decl_66,type,
    v16_lattices: $i > $o ).

tff(decl_67,type,
    v12_lattices: $i > $o ).

tff(decl_68,type,
    a_1_1_lopclset: $i > $i ).

tff(decl_69,type,
    l1_lattices: $i > $o ).

tff(decl_70,type,
    k5_lattices: $i > $i ).

tff(decl_71,type,
    l2_lattices: $i > $o ).

tff(decl_72,type,
    k7_lattices: ( $i * $i ) > $i ).

tff(decl_73,type,
    k8_lopclset: $i > $i ).

tff(decl_74,type,
    m2_relset_1: ( $i * $i * $i ) > $o ).

tff(decl_75,type,
    l1_struct_0: $i > $o ).

tff(decl_76,type,
    m1_filter_0: ( $i * $i ) > $o ).

tff(decl_77,type,
    k4_xboole_0: ( $i * $i ) > $i ).

tff(decl_78,type,
    k1_xboole_0: $i ).

tff(decl_79,type,
    v1_filter_0: ( $i * $i ) > $o ).

tff(decl_80,type,
    k1_funct_1: ( $i * $i ) > $i ).

tff(decl_81,type,
    r1_tarski: ( $i * $i ) > $o ).

tff(decl_82,type,
    esk1_0: $i ).

tff(decl_83,type,
    esk2_0: $i ).

tff(decl_84,type,
    esk3_0: $i ).

tff(decl_85,type,
    esk4_0: $i ).

tff(decl_86,type,
    esk5_0: $i ).

tff(decl_87,type,
    esk6_1: $i > $i ).

tff(decl_88,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_89,type,
    esk8_1: $i > $i ).

tff(decl_90,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_91,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_92,type,
    esk11_0: $i ).

tff(decl_93,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_94,type,
    esk13_0: $i ).

tff(decl_95,type,
    esk14_0: $i ).

tff(decl_96,type,
    esk15_2: ( $i * $i ) > $i ).

tff(decl_97,type,
    esk16_1: $i > $i ).

tff(decl_98,type,
    esk17_0: $i ).

tff(decl_99,type,
    esk18_1: $i > $i ).

tff(decl_100,type,
    esk19_1: $i > $i ).

tff(decl_101,type,
    esk20_2: ( $i * $i ) > $i ).

tff(decl_102,type,
    epred1_0: $o ).

tff(decl_103,type,
    epred2_0: $o ).

fof(t37_lopclset,conjecture,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & v17_lattices(X1)
        & ~ v3_realset2(X1)
        & l3_lattices(X1) )
     => k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k6_lattices(X1)) = k7_lopclset(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_lopclset) ).

fof(t37_lattice4,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & v17_lattices(X1)
        & l3_lattices(X1) )
     => k7_lattices(X1,k5_lattices(X1)) = k6_lattices(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_lattice4) ).

fof(t28_lopclset,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & v17_lattices(X1)
        & ~ v3_realset2(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => k4_xboole_0(k7_lopclset(X1),k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),X2)) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_lopclset) ).

fof(t36_lopclset,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & v17_lattices(X1)
        & ~ v3_realset2(X1)
        & l3_lattices(X1) )
     => k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k5_lattices(X1)) = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_lopclset) ).

fof(t3_boole,axiom,
    ! [X1] : k4_xboole_0(X1,k1_xboole_0) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).

fof(dt_k5_lattices,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & l1_lattices(X1) )
     => m1_subset_1(k5_lattices(X1),u1_struct_0(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattices) ).

fof(dt_l3_lattices,axiom,
    ! [X1] :
      ( l3_lattices(X1)
     => ( l1_lattices(X1)
        & l2_lattices(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ v3_struct_0(X1)
          & v10_lattices(X1)
          & v17_lattices(X1)
          & ~ v3_realset2(X1)
          & l3_lattices(X1) )
       => k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k6_lattices(X1)) = k7_lopclset(X1) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t37_lopclset])]) ).

fof(c_0_8,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & v17_lattices(X1)
        & l3_lattices(X1) )
     => k7_lattices(X1,k5_lattices(X1)) = k6_lattices(X1) ),
    inference(fof_simplification,[status(thm)],[t37_lattice4]) ).

fof(c_0_9,negated_conjecture,
    ( ~ v3_struct_0(esk1_0)
    & v10_lattices(esk1_0)
    & v17_lattices(esk1_0)
    & ~ v3_realset2(esk1_0)
    & l3_lattices(esk1_0)
    & k8_funct_2(u1_struct_0(esk1_0),k1_zfmisc_1(k7_lopclset(esk1_0)),k9_lopclset(esk1_0),k6_lattices(esk1_0)) != k7_lopclset(esk1_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_10,plain,
    ! [X147] :
      ( v3_struct_0(X147)
      | ~ v10_lattices(X147)
      | ~ v17_lattices(X147)
      | ~ l3_lattices(X147)
      | k7_lattices(X147,k5_lattices(X147)) = k6_lattices(X147) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).

fof(c_0_11,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & v17_lattices(X1)
        & ~ v3_realset2(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => k4_xboole_0(k7_lopclset(X1),k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),X2)) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,X2)) ) ),
    inference(fof_simplification,[status(thm)],[t28_lopclset]) ).

cnf(c_0_12,negated_conjecture,
    k8_funct_2(u1_struct_0(esk1_0),k1_zfmisc_1(k7_lopclset(esk1_0)),k9_lopclset(esk1_0),k6_lattices(esk1_0)) != k7_lopclset(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ( v3_struct_0(X1)
    | k7_lattices(X1,k5_lattices(X1)) = k6_lattices(X1)
    | ~ v10_lattices(X1)
    | ~ v17_lattices(X1)
    | ~ l3_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    l3_lattices(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,negated_conjecture,
    v17_lattices(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,negated_conjecture,
    v10_lattices(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_17,negated_conjecture,
    ~ v3_struct_0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_18,plain,
    ! [X139,X140] :
      ( v3_struct_0(X139)
      | ~ v10_lattices(X139)
      | ~ v17_lattices(X139)
      | v3_realset2(X139)
      | ~ l3_lattices(X139)
      | ~ m1_subset_1(X140,u1_struct_0(X139))
      | k4_xboole_0(k7_lopclset(X139),k8_funct_2(u1_struct_0(X139),k1_zfmisc_1(k7_lopclset(X139)),k9_lopclset(X139),X140)) = k8_funct_2(u1_struct_0(X139),k1_zfmisc_1(k7_lopclset(X139)),k9_lopclset(X139),k7_lattices(X139,X140)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).

fof(c_0_19,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & v17_lattices(X1)
        & ~ v3_realset2(X1)
        & l3_lattices(X1) )
     => k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k5_lattices(X1)) = k1_xboole_0 ),
    inference(fof_simplification,[status(thm)],[t36_lopclset]) ).

cnf(c_0_20,negated_conjecture,
    k8_funct_2(u1_struct_0(esk1_0),k1_zfmisc_1(k7_lopclset(esk1_0)),k9_lopclset(esk1_0),k7_lattices(esk1_0,k5_lattices(esk1_0))) != k7_lopclset(esk1_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]),c_0_16])]),c_0_17]) ).

cnf(c_0_21,plain,
    ( v3_struct_0(X1)
    | v3_realset2(X1)
    | k4_xboole_0(k7_lopclset(X1),k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),X2)) = k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k7_lattices(X1,X2))
    | ~ v10_lattices(X1)
    | ~ v17_lattices(X1)
    | ~ l3_lattices(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    ~ v3_realset2(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_23,plain,
    ! [X146] :
      ( v3_struct_0(X146)
      | ~ v10_lattices(X146)
      | ~ v17_lattices(X146)
      | v3_realset2(X146)
      | ~ l3_lattices(X146)
      | k8_funct_2(u1_struct_0(X146),k1_zfmisc_1(k7_lopclset(X146)),k9_lopclset(X146),k5_lattices(X146)) = k1_xboole_0 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).

fof(c_0_24,plain,
    ! [X148] : k4_xboole_0(X148,k1_xboole_0) = X148,
    inference(variable_rename,[status(thm)],[t3_boole]) ).

fof(c_0_25,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & l1_lattices(X1) )
     => m1_subset_1(k5_lattices(X1),u1_struct_0(X1)) ),
    inference(fof_simplification,[status(thm)],[dt_k5_lattices]) ).

fof(c_0_26,plain,
    ! [X71] :
      ( ( l1_lattices(X71)
        | ~ l3_lattices(X71) )
      & ( l2_lattices(X71)
        | ~ l3_lattices(X71) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).

cnf(c_0_27,negated_conjecture,
    ( k4_xboole_0(k7_lopclset(esk1_0),k8_funct_2(u1_struct_0(esk1_0),k1_zfmisc_1(k7_lopclset(esk1_0)),k9_lopclset(esk1_0),k5_lattices(esk1_0))) != k7_lopclset(esk1_0)
    | ~ m1_subset_1(k5_lattices(esk1_0),u1_struct_0(esk1_0)) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14]),c_0_15]),c_0_16])]),c_0_22]),c_0_17]) ).

cnf(c_0_28,plain,
    ( v3_struct_0(X1)
    | v3_realset2(X1)
    | k8_funct_2(u1_struct_0(X1),k1_zfmisc_1(k7_lopclset(X1)),k9_lopclset(X1),k5_lattices(X1)) = k1_xboole_0
    | ~ v10_lattices(X1)
    | ~ v17_lattices(X1)
    | ~ l3_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_29,plain,
    k4_xboole_0(X1,k1_xboole_0) = X1,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

fof(c_0_30,plain,
    ! [X58] :
      ( v3_struct_0(X58)
      | ~ l1_lattices(X58)
      | m1_subset_1(k5_lattices(X58),u1_struct_0(X58)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).

cnf(c_0_31,plain,
    ( l1_lattices(X1)
    | ~ l3_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_32,negated_conjecture,
    ~ m1_subset_1(k5_lattices(esk1_0),u1_struct_0(esk1_0)),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_14]),c_0_15]),c_0_16])]),c_0_22]),c_0_17]) ).

cnf(c_0_33,plain,
    ( v3_struct_0(X1)
    | m1_subset_1(k5_lattices(X1),u1_struct_0(X1))
    | ~ l1_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_34,negated_conjecture,
    l1_lattices(esk1_0),
    inference(spm,[status(thm)],[c_0_31,c_0_14]) ).

cnf(c_0_35,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),c_0_17]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LAT291+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n012.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 09:38:11 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.78  % Version  : CSE_E---1.5
% 0.20/0.78  % Problem  : theBenchmark.p
% 0.20/0.78  % Proof found
% 0.20/0.78  % SZS status Theorem for theBenchmark.p
% 0.20/0.78  % SZS output start Proof
% See solution above
% 0.59/0.78  % Total time : 0.183000 s
% 0.59/0.78  % SZS output end Proof
% 0.59/0.78  % Total time : 0.188000 s
%------------------------------------------------------------------------------