TSTP Solution File: LAT305+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT305+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n011.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 06:01:02 EDT 2023

% Result   : Theorem 3.31s 3.43s
% Output   : CNFRefutation 3.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   83
% Syntax   : Number of formulae    :  151 (  17 unt;  72 typ;   0 def)
%            Number of atoms       :  412 (  18 equ)
%            Maximal formula atoms :   28 (   5 avg)
%            Number of connectives :  531 ( 198   ~; 199   |;  99   &)
%                                         (   4 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   97 (  56   >;  41   *;   0   +;   0  <<)
%            Number of predicates  :   33 (  31 usr;   1 prp; 0-3 aty)
%            Number of functors    :   41 (  41 usr;  16 con; 0-6 aty)
%            Number of variables   :  122 (   1 sgn;  74   !;   3   ?;   0   :)

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

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

tff(decl_24,type,
    l3_lattices: $i > $o ).

tff(decl_25,type,
    u1_struct_0: $i > $i ).

tff(decl_26,type,
    m1_subset_1: ( $i * $i ) > $o ).

tff(decl_27,type,
    k18_filter_2: ( $i * $i ) > $i ).

tff(decl_28,type,
    r2_hidden: ( $i * $i ) > $o ).

tff(decl_29,type,
    k4_lattices: ( $i * $i * $i ) > $i ).

tff(decl_30,type,
    v1_xboole_0: $i > $o ).

tff(decl_31,type,
    v1_funct_1: $i > $o ).

tff(decl_32,type,
    v4_lattices: $i > $o ).

tff(decl_33,type,
    v5_lattices: $i > $o ).

tff(decl_34,type,
    v6_lattices: $i > $o ).

tff(decl_35,type,
    v7_lattices: $i > $o ).

tff(decl_36,type,
    v8_lattices: $i > $o ).

tff(decl_37,type,
    v9_lattices: $i > $o ).

tff(decl_38,type,
    v1_realset1: $i > $o ).

tff(decl_39,type,
    k2_zfmisc_1: ( $i * $i ) > $i ).

tff(decl_40,type,
    k1_zfmisc_1: $i > $i ).

tff(decl_41,type,
    v1_relat_1: $i > $o ).

tff(decl_42,type,
    v2_funct_1: $i > $o ).

tff(decl_43,type,
    k2_tarski: ( $i * $i ) > $i ).

tff(decl_44,type,
    l1_lattices: $i > $o ).

tff(decl_45,type,
    k1_binop_1: ( $i * $i * $i ) > $i ).

tff(decl_46,type,
    k4_tarski: ( $i * $i ) > $i ).

tff(decl_47,type,
    k1_funct_1: ( $i * $i ) > $i ).

tff(decl_48,type,
    k2_lattices: ( $i * $i * $i ) > $i ).

tff(decl_49,type,
    u1_lattices: $i > $i ).

tff(decl_50,type,
    k2_binop_1: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_51,type,
    k1_tarski: $i > $i ).

tff(decl_52,type,
    a_2_0_filter_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    m2_filter_2: ( $i * $i ) > $o ).

tff(decl_54,type,
    v1_funct_2: ( $i * $i * $i ) > $o ).

tff(decl_55,type,
    m1_relset_1: ( $i * $i * $i ) > $o ).

tff(decl_56,type,
    l1_struct_0: $i > $o ).

tff(decl_57,type,
    l2_lattices: $i > $o ).

tff(decl_58,type,
    m2_lattice4: ( $i * $i ) > $o ).

tff(decl_59,type,
    m2_relset_1: ( $i * $i * $i ) > $o ).

tff(decl_60,type,
    k1_xboole_0: $i ).

tff(decl_61,type,
    v1_finset_1: $i > $o ).

tff(decl_62,type,
    v1_binop_1: ( $i * $i ) > $o ).

tff(decl_63,type,
    v1_partfun1: ( $i * $i * $i ) > $o ).

tff(decl_64,type,
    v2_binop_1: ( $i * $i ) > $o ).

tff(decl_65,type,
    r3_lattices: ( $i * $i * $i ) > $o ).

tff(decl_66,type,
    r1_lattices: ( $i * $i * $i ) > $o ).

tff(decl_67,type,
    r1_tarski: ( $i * $i ) > $o ).

tff(decl_68,type,
    esk1_0: $i ).

tff(decl_69,type,
    esk2_0: $i ).

tff(decl_70,type,
    esk3_0: $i ).

tff(decl_71,type,
    esk4_0: $i ).

tff(decl_72,type,
    esk5_0: $i ).

tff(decl_73,type,
    esk6_0: $i ).

tff(decl_74,type,
    esk7_0: $i ).

tff(decl_75,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_76,type,
    esk9_1: $i > $i ).

tff(decl_77,type,
    esk10_1: $i > $i ).

tff(decl_78,type,
    esk11_1: $i > $i ).

tff(decl_79,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_80,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk14_0: $i ).

tff(decl_82,type,
    esk15_1: $i > $i ).

tff(decl_83,type,
    esk16_0: $i ).

tff(decl_84,type,
    esk17_1: $i > $i ).

tff(decl_85,type,
    esk18_0: $i ).

tff(decl_86,type,
    esk19_0: $i ).

tff(decl_87,type,
    esk20_0: $i ).

tff(decl_88,type,
    esk21_1: $i > $i ).

tff(decl_89,type,
    esk22_0: $i ).

tff(decl_90,type,
    esk23_0: $i ).

tff(decl_91,type,
    esk24_0: $i ).

tff(decl_92,type,
    esk25_1: $i > $i ).

tff(decl_93,type,
    esk26_2: ( $i * $i ) > $i ).

fof(reflexivity_r3_lattices,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X1)
        & v6_lattices(X1)
        & v8_lattices(X1)
        & v9_lattices(X1)
        & l3_lattices(X1)
        & m1_subset_1(X2,u1_struct_0(X1))
        & m1_subset_1(X3,u1_struct_0(X1)) )
     => r3_lattices(X1,X2,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).

fof(commutativity_k4_lattices,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X1)
        & v6_lattices(X1)
        & l1_lattices(X1)
        & m1_subset_1(X2,u1_struct_0(X1))
        & m1_subset_1(X3,u1_struct_0(X1)) )
     => k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).

fof(t31_filter_2,conjecture,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X1))
             => ( r2_hidden(X2,k18_filter_2(X1,X2))
                & r2_hidden(k4_lattices(X1,X2,X3),k18_filter_2(X1,X2))
                & r2_hidden(k4_lattices(X1,X3,X2),k18_filter_2(X1,X2)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_filter_2) ).

fof(existence_m1_subset_1,axiom,
    ! [X1] :
    ? [X2] : m1_subset_1(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(redefinition_r3_lattices,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X1)
        & v6_lattices(X1)
        & v8_lattices(X1)
        & v9_lattices(X1)
        & l3_lattices(X1)
        & m1_subset_1(X2,u1_struct_0(X1))
        & m1_subset_1(X3,u1_struct_0(X1)) )
     => ( r3_lattices(X1,X2,X3)
      <=> r1_lattices(X1,X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).

fof(t23_lattices,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v6_lattices(X1)
        & v8_lattices(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X1))
             => r1_lattices(X1,k4_lattices(X1,X2,X3),X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattices) ).

fof(dt_k4_lattices,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X1)
        & v6_lattices(X1)
        & l1_lattices(X1)
        & m1_subset_1(X2,u1_struct_0(X1))
        & m1_subset_1(X3,u1_struct_0(X1)) )
     => m1_subset_1(k4_lattices(X1,X2,X3),u1_struct_0(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattices) ).

fof(cc1_lattices,axiom,
    ! [X1] :
      ( l3_lattices(X1)
     => ( ( ~ v3_struct_0(X1)
          & v10_lattices(X1) )
       => ( ~ v3_struct_0(X1)
          & v4_lattices(X1)
          & v5_lattices(X1)
          & v6_lattices(X1)
          & v7_lattices(X1)
          & v8_lattices(X1)
          & v9_lattices(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).

fof(d9_filter_2,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_2) ).

fof(dt_l3_lattices,axiom,
    ! [X1] :
      ( l3_lattices(X1)
     => ( l1_lattices(X1)
        & l2_lattices(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).

fof(fraenkel_a_2_0_filter_2,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X2)
        & v10_lattices(X2)
        & l3_lattices(X2)
        & m1_subset_1(X3,u1_struct_0(X2)) )
     => ( r2_hidden(X1,a_2_0_filter_2(X2,X3))
      <=> ? [X4] :
            ( m1_subset_1(X4,u1_struct_0(X2))
            & X1 = X4
            & r3_lattices(X2,X4,X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_2) ).

fof(c_0_11,plain,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X1)
        & v6_lattices(X1)
        & v8_lattices(X1)
        & v9_lattices(X1)
        & l3_lattices(X1)
        & m1_subset_1(X2,u1_struct_0(X1))
        & m1_subset_1(X3,u1_struct_0(X1)) )
     => r3_lattices(X1,X2,X2) ),
    inference(fof_simplification,[status(thm)],[reflexivity_r3_lattices]) ).

fof(c_0_12,plain,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X1)
        & v6_lattices(X1)
        & l1_lattices(X1)
        & m1_subset_1(X2,u1_struct_0(X1))
        & m1_subset_1(X3,u1_struct_0(X1)) )
     => k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2) ),
    inference(fof_simplification,[status(thm)],[commutativity_k4_lattices]) ).

fof(c_0_13,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ v3_struct_0(X1)
          & v10_lattices(X1)
          & l3_lattices(X1) )
       => ! [X2] :
            ( m1_subset_1(X2,u1_struct_0(X1))
           => ! [X3] :
                ( m1_subset_1(X3,u1_struct_0(X1))
               => ( r2_hidden(X2,k18_filter_2(X1,X2))
                  & r2_hidden(k4_lattices(X1,X2,X3),k18_filter_2(X1,X2))
                  & r2_hidden(k4_lattices(X1,X3,X2),k18_filter_2(X1,X2)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t31_filter_2])]) ).

fof(c_0_14,plain,
    ! [X123,X124,X125] :
      ( v3_struct_0(X123)
      | ~ v6_lattices(X123)
      | ~ v8_lattices(X123)
      | ~ v9_lattices(X123)
      | ~ l3_lattices(X123)
      | ~ m1_subset_1(X124,u1_struct_0(X123))
      | ~ m1_subset_1(X125,u1_struct_0(X123))
      | r3_lattices(X123,X124,X124) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).

fof(c_0_15,plain,
    ! [X67] : m1_subset_1(esk9_1(X67),X67),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).

fof(c_0_16,plain,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X1)
        & v6_lattices(X1)
        & v8_lattices(X1)
        & v9_lattices(X1)
        & l3_lattices(X1)
        & m1_subset_1(X2,u1_struct_0(X1))
        & m1_subset_1(X3,u1_struct_0(X1)) )
     => ( r3_lattices(X1,X2,X3)
      <=> r1_lattices(X1,X2,X3) ) ),
    inference(fof_simplification,[status(thm)],[redefinition_r3_lattices]) ).

fof(c_0_17,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v6_lattices(X1)
        & v8_lattices(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => ! [X3] :
              ( m1_subset_1(X3,u1_struct_0(X1))
             => r1_lattices(X1,k4_lattices(X1,X2,X3),X2) ) ) ),
    inference(fof_simplification,[status(thm)],[t23_lattices]) ).

fof(c_0_18,plain,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X1)
        & v6_lattices(X1)
        & l1_lattices(X1)
        & m1_subset_1(X2,u1_struct_0(X1))
        & m1_subset_1(X3,u1_struct_0(X1)) )
     => m1_subset_1(k4_lattices(X1,X2,X3),u1_struct_0(X1)) ),
    inference(fof_simplification,[status(thm)],[dt_k4_lattices]) ).

fof(c_0_19,plain,
    ! [X22,X23,X24] :
      ( v3_struct_0(X22)
      | ~ v6_lattices(X22)
      | ~ l1_lattices(X22)
      | ~ m1_subset_1(X23,u1_struct_0(X22))
      | ~ m1_subset_1(X24,u1_struct_0(X22))
      | k4_lattices(X22,X23,X24) = k4_lattices(X22,X24,X23) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).

fof(c_0_20,negated_conjecture,
    ( ~ v3_struct_0(esk1_0)
    & v10_lattices(esk1_0)
    & l3_lattices(esk1_0)
    & m1_subset_1(esk2_0,u1_struct_0(esk1_0))
    & m1_subset_1(esk3_0,u1_struct_0(esk1_0))
    & ( ~ r2_hidden(esk2_0,k18_filter_2(esk1_0,esk2_0))
      | ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),k18_filter_2(esk1_0,esk2_0))
      | ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),k18_filter_2(esk1_0,esk2_0)) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).

cnf(c_0_21,plain,
    ( v3_struct_0(X1)
    | r3_lattices(X1,X2,X2)
    | ~ v6_lattices(X1)
    | ~ v8_lattices(X1)
    | ~ v9_lattices(X1)
    | ~ l3_lattices(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1))
    | ~ m1_subset_1(X3,u1_struct_0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,plain,
    m1_subset_1(esk9_1(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_23,plain,
    ! [X1] :
      ( l3_lattices(X1)
     => ( ( ~ v3_struct_0(X1)
          & v10_lattices(X1) )
       => ( ~ v3_struct_0(X1)
          & v4_lattices(X1)
          & v5_lattices(X1)
          & v6_lattices(X1)
          & v7_lattices(X1)
          & v8_lattices(X1)
          & v9_lattices(X1) ) ) ),
    inference(fof_simplification,[status(thm)],[cc1_lattices]) ).

fof(c_0_24,plain,
    ! [X119,X120,X121] :
      ( ( ~ r3_lattices(X119,X120,X121)
        | r1_lattices(X119,X120,X121)
        | v3_struct_0(X119)
        | ~ v6_lattices(X119)
        | ~ v8_lattices(X119)
        | ~ v9_lattices(X119)
        | ~ l3_lattices(X119)
        | ~ m1_subset_1(X120,u1_struct_0(X119))
        | ~ m1_subset_1(X121,u1_struct_0(X119)) )
      & ( ~ r1_lattices(X119,X120,X121)
        | r3_lattices(X119,X120,X121)
        | v3_struct_0(X119)
        | ~ v6_lattices(X119)
        | ~ v8_lattices(X119)
        | ~ v9_lattices(X119)
        | ~ l3_lattices(X119)
        | ~ m1_subset_1(X120,u1_struct_0(X119))
        | ~ m1_subset_1(X121,u1_struct_0(X119)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).

fof(c_0_25,plain,
    ! [X128,X129,X130] :
      ( v3_struct_0(X128)
      | ~ v6_lattices(X128)
      | ~ v8_lattices(X128)
      | ~ l3_lattices(X128)
      | ~ m1_subset_1(X129,u1_struct_0(X128))
      | ~ m1_subset_1(X130,u1_struct_0(X128))
      | r1_lattices(X128,k4_lattices(X128,X129,X130),X129) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).

fof(c_0_26,plain,
    ! [X46,X47,X48] :
      ( v3_struct_0(X46)
      | ~ v6_lattices(X46)
      | ~ l1_lattices(X46)
      | ~ m1_subset_1(X47,u1_struct_0(X46))
      | ~ m1_subset_1(X48,u1_struct_0(X46))
      | m1_subset_1(k4_lattices(X46,X47,X48),u1_struct_0(X46)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).

fof(c_0_27,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v10_lattices(X1)
        & l3_lattices(X1) )
     => ! [X2] :
          ( m1_subset_1(X2,u1_struct_0(X1))
         => k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2) ) ),
    inference(fof_simplification,[status(thm)],[d9_filter_2]) ).

cnf(c_0_28,plain,
    ( v3_struct_0(X1)
    | k4_lattices(X1,X2,X3) = k4_lattices(X1,X3,X2)
    | ~ v6_lattices(X1)
    | ~ l1_lattices(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1))
    | ~ m1_subset_1(X3,u1_struct_0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_29,negated_conjecture,
    m1_subset_1(esk3_0,u1_struct_0(esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_30,negated_conjecture,
    ~ v3_struct_0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_31,plain,
    ! [X51] :
      ( ( l1_lattices(X51)
        | ~ l3_lattices(X51) )
      & ( l2_lattices(X51)
        | ~ l3_lattices(X51) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).

fof(c_0_32,plain,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X2)
        & v10_lattices(X2)
        & l3_lattices(X2)
        & m1_subset_1(X3,u1_struct_0(X2)) )
     => ( r2_hidden(X1,a_2_0_filter_2(X2,X3))
      <=> ? [X4] :
            ( m1_subset_1(X4,u1_struct_0(X2))
            & X1 = X4
            & r3_lattices(X2,X4,X3) ) ) ),
    inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_filter_2]) ).

cnf(c_0_33,plain,
    ( r3_lattices(X1,X2,X2)
    | v3_struct_0(X1)
    | ~ v9_lattices(X1)
    | ~ v8_lattices(X1)
    | ~ v6_lattices(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1))
    | ~ l3_lattices(X1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_34,negated_conjecture,
    m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_35,negated_conjecture,
    l3_lattices(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_36,plain,
    ! [X13] :
      ( ( ~ v3_struct_0(X13)
        | v3_struct_0(X13)
        | ~ v10_lattices(X13)
        | ~ l3_lattices(X13) )
      & ( v4_lattices(X13)
        | v3_struct_0(X13)
        | ~ v10_lattices(X13)
        | ~ l3_lattices(X13) )
      & ( v5_lattices(X13)
        | v3_struct_0(X13)
        | ~ v10_lattices(X13)
        | ~ l3_lattices(X13) )
      & ( v6_lattices(X13)
        | v3_struct_0(X13)
        | ~ v10_lattices(X13)
        | ~ l3_lattices(X13) )
      & ( v7_lattices(X13)
        | v3_struct_0(X13)
        | ~ v10_lattices(X13)
        | ~ l3_lattices(X13) )
      & ( v8_lattices(X13)
        | v3_struct_0(X13)
        | ~ v10_lattices(X13)
        | ~ l3_lattices(X13) )
      & ( v9_lattices(X13)
        | v3_struct_0(X13)
        | ~ v10_lattices(X13)
        | ~ l3_lattices(X13) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).

cnf(c_0_37,plain,
    ( r3_lattices(X1,X2,X3)
    | v3_struct_0(X1)
    | ~ r1_lattices(X1,X2,X3)
    | ~ v6_lattices(X1)
    | ~ v8_lattices(X1)
    | ~ v9_lattices(X1)
    | ~ l3_lattices(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1))
    | ~ m1_subset_1(X3,u1_struct_0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_38,plain,
    ( v3_struct_0(X1)
    | r1_lattices(X1,k4_lattices(X1,X2,X3),X2)
    | ~ v6_lattices(X1)
    | ~ v8_lattices(X1)
    | ~ l3_lattices(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1))
    | ~ m1_subset_1(X3,u1_struct_0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_39,plain,
    ( v3_struct_0(X1)
    | m1_subset_1(k4_lattices(X1,X2,X3),u1_struct_0(X1))
    | ~ v6_lattices(X1)
    | ~ l1_lattices(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1))
    | ~ m1_subset_1(X3,u1_struct_0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

fof(c_0_40,plain,
    ! [X33,X34] :
      ( v3_struct_0(X33)
      | ~ v10_lattices(X33)
      | ~ l3_lattices(X33)
      | ~ m1_subset_1(X34,u1_struct_0(X33))
      | k18_filter_2(X33,X34) = a_2_0_filter_2(X33,X34) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).

cnf(c_0_41,negated_conjecture,
    ( k4_lattices(esk1_0,X1,esk3_0) = k4_lattices(esk1_0,esk3_0,X1)
    | ~ l1_lattices(esk1_0)
    | ~ v6_lattices(esk1_0)
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).

cnf(c_0_42,plain,
    ( l1_lattices(X1)
    | ~ l3_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

fof(c_0_43,plain,
    ! [X86,X87,X88,X90] :
      ( ( m1_subset_1(esk13_3(X86,X87,X88),u1_struct_0(X87))
        | ~ r2_hidden(X86,a_2_0_filter_2(X87,X88))
        | v3_struct_0(X87)
        | ~ v10_lattices(X87)
        | ~ l3_lattices(X87)
        | ~ m1_subset_1(X88,u1_struct_0(X87)) )
      & ( X86 = esk13_3(X86,X87,X88)
        | ~ r2_hidden(X86,a_2_0_filter_2(X87,X88))
        | v3_struct_0(X87)
        | ~ v10_lattices(X87)
        | ~ l3_lattices(X87)
        | ~ m1_subset_1(X88,u1_struct_0(X87)) )
      & ( r3_lattices(X87,esk13_3(X86,X87,X88),X88)
        | ~ r2_hidden(X86,a_2_0_filter_2(X87,X88))
        | v3_struct_0(X87)
        | ~ v10_lattices(X87)
        | ~ l3_lattices(X87)
        | ~ m1_subset_1(X88,u1_struct_0(X87)) )
      & ( ~ m1_subset_1(X90,u1_struct_0(X87))
        | X86 != X90
        | ~ r3_lattices(X87,X90,X88)
        | r2_hidden(X86,a_2_0_filter_2(X87,X88))
        | v3_struct_0(X87)
        | ~ v10_lattices(X87)
        | ~ l3_lattices(X87)
        | ~ m1_subset_1(X88,u1_struct_0(X87)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])])]) ).

cnf(c_0_44,negated_conjecture,
    ( r3_lattices(esk1_0,esk2_0,esk2_0)
    | ~ v9_lattices(esk1_0)
    | ~ v8_lattices(esk1_0)
    | ~ v6_lattices(esk1_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),c_0_30]) ).

cnf(c_0_45,plain,
    ( v9_lattices(X1)
    | v3_struct_0(X1)
    | ~ v10_lattices(X1)
    | ~ l3_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_46,negated_conjecture,
    v10_lattices(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_47,negated_conjecture,
    ( r3_lattices(esk1_0,X1,esk2_0)
    | ~ r1_lattices(esk1_0,X1,esk2_0)
    | ~ v9_lattices(esk1_0)
    | ~ v8_lattices(esk1_0)
    | ~ v6_lattices(esk1_0)
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_34]),c_0_35])]),c_0_30]) ).

cnf(c_0_48,negated_conjecture,
    ( r1_lattices(esk1_0,k4_lattices(esk1_0,X1,esk3_0),X1)
    | ~ v8_lattices(esk1_0)
    | ~ v6_lattices(esk1_0)
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_29]),c_0_35])]),c_0_30]) ).

cnf(c_0_49,plain,
    ( v8_lattices(X1)
    | v3_struct_0(X1)
    | ~ v10_lattices(X1)
    | ~ l3_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_50,negated_conjecture,
    ( m1_subset_1(k4_lattices(esk1_0,X1,esk3_0),u1_struct_0(esk1_0))
    | ~ l1_lattices(esk1_0)
    | ~ v6_lattices(esk1_0)
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_29]),c_0_30]) ).

cnf(c_0_51,plain,
    ( v3_struct_0(X1)
    | k18_filter_2(X1,X2) = a_2_0_filter_2(X1,X2)
    | ~ v10_lattices(X1)
    | ~ l3_lattices(X1)
    | ~ m1_subset_1(X2,u1_struct_0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_52,negated_conjecture,
    ( k4_lattices(esk1_0,X1,esk3_0) = k4_lattices(esk1_0,esk3_0,X1)
    | ~ v6_lattices(esk1_0)
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_35])]) ).

cnf(c_0_53,plain,
    ( v6_lattices(X1)
    | v3_struct_0(X1)
    | ~ v10_lattices(X1)
    | ~ l3_lattices(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_54,plain,
    ( r2_hidden(X3,a_2_0_filter_2(X2,X4))
    | v3_struct_0(X2)
    | ~ m1_subset_1(X1,u1_struct_0(X2))
    | X3 != X1
    | ~ r3_lattices(X2,X1,X4)
    | ~ v10_lattices(X2)
    | ~ l3_lattices(X2)
    | ~ m1_subset_1(X4,u1_struct_0(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_55,negated_conjecture,
    ( r3_lattices(esk1_0,esk2_0,esk2_0)
    | ~ v8_lattices(esk1_0)
    | ~ v6_lattices(esk1_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_35]),c_0_46])]),c_0_30]) ).

cnf(c_0_56,negated_conjecture,
    ( r3_lattices(esk1_0,X1,esk2_0)
    | ~ r1_lattices(esk1_0,X1,esk2_0)
    | ~ v8_lattices(esk1_0)
    | ~ v6_lattices(esk1_0)
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_45]),c_0_35]),c_0_46])]),c_0_30]) ).

cnf(c_0_57,negated_conjecture,
    ( r1_lattices(esk1_0,k4_lattices(esk1_0,X1,esk3_0),X1)
    | ~ v6_lattices(esk1_0)
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_35]),c_0_46])]),c_0_30]) ).

cnf(c_0_58,negated_conjecture,
    ( m1_subset_1(k4_lattices(esk1_0,X1,esk3_0),u1_struct_0(esk1_0))
    | ~ v6_lattices(esk1_0)
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_42]),c_0_35])]) ).

cnf(c_0_59,negated_conjecture,
    ( ~ r2_hidden(esk2_0,k18_filter_2(esk1_0,esk2_0))
    | ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),k18_filter_2(esk1_0,esk2_0))
    | ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),k18_filter_2(esk1_0,esk2_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_60,negated_conjecture,
    k18_filter_2(esk1_0,esk2_0) = a_2_0_filter_2(esk1_0,esk2_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_34]),c_0_35]),c_0_46])]),c_0_30]) ).

cnf(c_0_61,negated_conjecture,
    ( k4_lattices(esk1_0,X1,esk3_0) = k4_lattices(esk1_0,esk3_0,X1)
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_35]),c_0_46])]),c_0_30]) ).

cnf(c_0_62,plain,
    ( r2_hidden(X1,a_2_0_filter_2(X2,X3))
    | v3_struct_0(X2)
    | ~ r3_lattices(X2,X1,X3)
    | ~ m1_subset_1(X3,u1_struct_0(X2))
    | ~ m1_subset_1(X1,u1_struct_0(X2))
    | ~ l3_lattices(X2)
    | ~ v10_lattices(X2) ),
    inference(er,[status(thm)],[c_0_54]) ).

cnf(c_0_63,negated_conjecture,
    ( r3_lattices(esk1_0,esk2_0,esk2_0)
    | ~ v6_lattices(esk1_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_49]),c_0_35]),c_0_46])]),c_0_30]) ).

cnf(c_0_64,negated_conjecture,
    ( r3_lattices(esk1_0,X1,esk2_0)
    | ~ r1_lattices(esk1_0,X1,esk2_0)
    | ~ v6_lattices(esk1_0)
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_49]),c_0_35]),c_0_46])]),c_0_30]) ).

cnf(c_0_65,negated_conjecture,
    ( r1_lattices(esk1_0,k4_lattices(esk1_0,X1,esk3_0),X1)
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_53]),c_0_35]),c_0_46])]),c_0_30]) ).

cnf(c_0_66,negated_conjecture,
    ( m1_subset_1(k4_lattices(esk1_0,X1,esk3_0),u1_struct_0(esk1_0))
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_53]),c_0_35]),c_0_46])]),c_0_30]) ).

cnf(c_0_67,negated_conjecture,
    ( ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),a_2_0_filter_2(esk1_0,esk2_0))
    | ~ r2_hidden(k4_lattices(esk1_0,esk3_0,esk2_0),a_2_0_filter_2(esk1_0,esk2_0))
    | ~ r2_hidden(esk2_0,a_2_0_filter_2(esk1_0,esk2_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_60]),c_0_60]) ).

cnf(c_0_68,negated_conjecture,
    k4_lattices(esk1_0,esk3_0,esk2_0) = k4_lattices(esk1_0,esk2_0,esk3_0),
    inference(spm,[status(thm)],[c_0_61,c_0_34]) ).

cnf(c_0_69,negated_conjecture,
    ( r2_hidden(X1,a_2_0_filter_2(esk1_0,esk2_0))
    | ~ r3_lattices(esk1_0,X1,esk2_0)
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_34]),c_0_35]),c_0_46])]),c_0_30]) ).

cnf(c_0_70,negated_conjecture,
    r3_lattices(esk1_0,esk2_0,esk2_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_53]),c_0_35]),c_0_46])]),c_0_30]) ).

cnf(c_0_71,negated_conjecture,
    ( r3_lattices(esk1_0,X1,esk2_0)
    | ~ r1_lattices(esk1_0,X1,esk2_0)
    | ~ m1_subset_1(X1,u1_struct_0(esk1_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_53]),c_0_35]),c_0_46])]),c_0_30]) ).

cnf(c_0_72,negated_conjecture,
    r1_lattices(esk1_0,k4_lattices(esk1_0,esk2_0,esk3_0),esk2_0),
    inference(spm,[status(thm)],[c_0_65,c_0_34]) ).

cnf(c_0_73,negated_conjecture,
    m1_subset_1(k4_lattices(esk1_0,esk2_0,esk3_0),u1_struct_0(esk1_0)),
    inference(spm,[status(thm)],[c_0_66,c_0_34]) ).

cnf(c_0_74,negated_conjecture,
    ( ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),a_2_0_filter_2(esk1_0,esk2_0))
    | ~ r2_hidden(esk2_0,a_2_0_filter_2(esk1_0,esk2_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).

cnf(c_0_75,negated_conjecture,
    r2_hidden(esk2_0,a_2_0_filter_2(esk1_0,esk2_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_34])]) ).

cnf(c_0_76,negated_conjecture,
    r3_lattices(esk1_0,k4_lattices(esk1_0,esk2_0,esk3_0),esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).

cnf(c_0_77,negated_conjecture,
    ~ r2_hidden(k4_lattices(esk1_0,esk2_0,esk3_0),a_2_0_filter_2(esk1_0,esk2_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).

cnf(c_0_78,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_76]),c_0_73])]),c_0_77]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LAT305+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n011.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 07:12:37 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 3.31/3.43  % Version  : CSE_E---1.5
% 3.31/3.43  % Problem  : theBenchmark.p
% 3.31/3.43  % Proof found
% 3.31/3.43  % SZS status Theorem for theBenchmark.p
% 3.31/3.43  % SZS output start Proof
% See solution above
% 3.31/3.44  % Total time : 2.837000 s
% 3.31/3.44  % SZS output end Proof
% 3.31/3.44  % Total time : 2.842000 s
%------------------------------------------------------------------------------