TSTP Solution File: SEU391+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU391+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n006.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 16:25:23 EDT 2023

% Result   : Theorem 0.21s 0.63s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   89
% Syntax   : Number of formulae    :  121 (   9 unt;  86 typ;   0 def)
%            Number of atoms       :  152 (  14 equ)
%            Maximal formula atoms :   26 (   4 avg)
%            Number of connectives :  182 (  65   ~;  74   |;  29   &)
%                                         (   4 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   90 (  67   >;  23   *;   0   +;   0  <<)
%            Number of predicates  :   40 (  38 usr;   1 prp; 0-3 aty)
%            Number of functors    :   48 (  48 usr;  19 con; 0-3 aty)
%            Number of variables   :   45 (   0 sgn;  22   !;   2   ?;   0   :)

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

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

tff(decl_24,type,
    the_carrier: $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(decl_43,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

tff(decl_51,type,
    a_2_1_yellow19: ( $i * $i ) > $i ).

tff(decl_52,type,
    relation_of2: ( $i * $i * $i ) > $o ).

tff(decl_53,type,
    cast_as_carrier_subset: $i > $i ).

tff(decl_54,type,
    boole_POSet: $i > $i ).

tff(decl_55,type,
    relation_of2_as_subset: ( $i * $i * $i ) > $o ).

tff(decl_56,type,
    empty_set: $i ).

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

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

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

tff(decl_60,type,
    v1_yellow_3: $i > $o ).

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

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

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

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

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

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

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

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

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

tff(decl_70,type,
    esk1_0: $i ).

tff(decl_71,type,
    esk2_0: $i ).

tff(decl_72,type,
    esk3_1: $i > $i ).

tff(decl_73,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_74,type,
    esk5_1: $i > $i ).

tff(decl_75,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_76,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk8_1: $i > $i ).

tff(decl_78,type,
    esk9_1: $i > $i ).

tff(decl_79,type,
    esk10_0: $i ).

tff(decl_80,type,
    esk11_0: $i ).

tff(decl_81,type,
    esk12_0: $i ).

tff(decl_82,type,
    esk13_0: $i ).

tff(decl_83,type,
    esk14_0: $i ).

tff(decl_84,type,
    esk15_1: $i > $i ).

tff(decl_85,type,
    esk16_1: $i > $i ).

tff(decl_86,type,
    esk17_0: $i ).

tff(decl_87,type,
    esk18_0: $i ).

tff(decl_88,type,
    esk19_0: $i ).

tff(decl_89,type,
    esk20_0: $i ).

tff(decl_90,type,
    esk21_1: $i > $i ).

tff(decl_91,type,
    esk22_1: $i > $i ).

tff(decl_92,type,
    esk23_1: $i > $i ).

tff(decl_93,type,
    esk24_0: $i ).

tff(decl_94,type,
    esk25_1: $i > $i ).

tff(decl_95,type,
    esk26_0: $i ).

tff(decl_96,type,
    esk27_0: $i ).

tff(decl_97,type,
    esk28_1: $i > $i ).

tff(decl_98,type,
    esk29_1: $i > $i ).

tff(decl_99,type,
    esk30_0: $i ).

tff(decl_100,type,
    esk31_1: $i > $i ).

tff(decl_101,type,
    esk32_1: $i > $i ).

tff(decl_102,type,
    esk33_1: $i > $i ).

tff(decl_103,type,
    esk34_1: $i > $i ).

tff(decl_104,type,
    esk35_0: $i ).

tff(decl_105,type,
    esk36_0: $i ).

tff(decl_106,type,
    esk37_0: $i ).

tff(decl_107,type,
    esk38_2: ( $i * $i ) > $i ).

fof(d3_yellow19,axiom,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ! [X2] :
          ( ( ~ empty_carrier(X2)
            & net_str(X2,X1) )
         => filter_of_net_str(X1,X2) = a_2_1_yellow19(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_yellow19) ).

fof(t11_yellow19,conjecture,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ! [X2] :
          ( ( ~ empty_carrier(X2)
            & net_str(X2,X1) )
         => ! [X3] :
              ( in(X3,filter_of_net_str(X1,X2))
            <=> ( is_eventually_in(X1,X2,X3)
                & element(X3,powerset(the_carrier(X1))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_yellow19) ).

fof(fraenkel_a_2_1_yellow19,axiom,
    ! [X1,X2,X3] :
      ( ( ~ empty_carrier(X2)
        & one_sorted_str(X2)
        & ~ empty_carrier(X3)
        & net_str(X3,X2) )
     => ( in(X1,a_2_1_yellow19(X2,X3))
      <=> ? [X4] :
            ( element(X4,powerset(the_carrier(X2)))
            & X1 = X4
            & is_eventually_in(X2,X3,X4) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_yellow19) ).

fof(c_0_3,plain,
    ! [X1] :
      ( ( ~ empty_carrier(X1)
        & one_sorted_str(X1) )
     => ! [X2] :
          ( ( ~ empty_carrier(X2)
            & net_str(X2,X1) )
         => filter_of_net_str(X1,X2) = a_2_1_yellow19(X1,X2) ) ),
    inference(fof_simplification,[status(thm)],[d3_yellow19]) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty_carrier(X1)
          & one_sorted_str(X1) )
       => ! [X2] :
            ( ( ~ empty_carrier(X2)
              & net_str(X2,X1) )
           => ! [X3] :
                ( in(X3,filter_of_net_str(X1,X2))
              <=> ( is_eventually_in(X1,X2,X3)
                  & element(X3,powerset(the_carrier(X1))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t11_yellow19])]) ).

fof(c_0_5,plain,
    ! [X1,X2,X3] :
      ( ( ~ empty_carrier(X2)
        & one_sorted_str(X2)
        & ~ empty_carrier(X3)
        & net_str(X3,X2) )
     => ( in(X1,a_2_1_yellow19(X2,X3))
      <=> ? [X4] :
            ( element(X4,powerset(the_carrier(X2)))
            & X1 = X4
            & is_eventually_in(X2,X3,X4) ) ) ),
    inference(fof_simplification,[status(thm)],[fraenkel_a_2_1_yellow19]) ).

fof(c_0_6,plain,
    ! [X29,X30] :
      ( empty_carrier(X29)
      | ~ one_sorted_str(X29)
      | empty_carrier(X30)
      | ~ net_str(X30,X29)
      | filter_of_net_str(X29,X30) = a_2_1_yellow19(X29,X30) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_7,negated_conjecture,
    ( ~ empty_carrier(esk35_0)
    & one_sorted_str(esk35_0)
    & ~ empty_carrier(esk36_0)
    & net_str(esk36_0,esk35_0)
    & ( ~ in(esk37_0,filter_of_net_str(esk35_0,esk36_0))
      | ~ is_eventually_in(esk35_0,esk36_0,esk37_0)
      | ~ element(esk37_0,powerset(the_carrier(esk35_0))) )
    & ( is_eventually_in(esk35_0,esk36_0,esk37_0)
      | in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) )
    & ( element(esk37_0,powerset(the_carrier(esk35_0)))
      | in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).

fof(c_0_8,plain,
    ! [X74,X75,X76,X78] :
      ( ( element(esk7_3(X74,X75,X76),powerset(the_carrier(X75)))
        | ~ in(X74,a_2_1_yellow19(X75,X76))
        | empty_carrier(X75)
        | ~ one_sorted_str(X75)
        | empty_carrier(X76)
        | ~ net_str(X76,X75) )
      & ( X74 = esk7_3(X74,X75,X76)
        | ~ in(X74,a_2_1_yellow19(X75,X76))
        | empty_carrier(X75)
        | ~ one_sorted_str(X75)
        | empty_carrier(X76)
        | ~ net_str(X76,X75) )
      & ( is_eventually_in(X75,X76,esk7_3(X74,X75,X76))
        | ~ in(X74,a_2_1_yellow19(X75,X76))
        | empty_carrier(X75)
        | ~ one_sorted_str(X75)
        | empty_carrier(X76)
        | ~ net_str(X76,X75) )
      & ( ~ element(X78,powerset(the_carrier(X75)))
        | X74 != X78
        | ~ is_eventually_in(X75,X76,X78)
        | in(X74,a_2_1_yellow19(X75,X76))
        | empty_carrier(X75)
        | ~ one_sorted_str(X75)
        | empty_carrier(X76)
        | ~ net_str(X76,X75) ) ),
    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_5])])])])]) ).

cnf(c_0_9,plain,
    ( empty_carrier(X1)
    | empty_carrier(X2)
    | filter_of_net_str(X1,X2) = a_2_1_yellow19(X1,X2)
    | ~ one_sorted_str(X1)
    | ~ net_str(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    net_str(esk36_0,esk35_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,negated_conjecture,
    one_sorted_str(esk35_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,negated_conjecture,
    ~ empty_carrier(esk36_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,negated_conjecture,
    ~ empty_carrier(esk35_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_14,plain,
    ( is_eventually_in(X1,X2,esk7_3(X3,X1,X2))
    | empty_carrier(X1)
    | empty_carrier(X2)
    | ~ in(X3,a_2_1_yellow19(X1,X2))
    | ~ one_sorted_str(X1)
    | ~ net_str(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    a_2_1_yellow19(esk35_0,esk36_0) = filter_of_net_str(esk35_0,esk36_0),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]),c_0_12]),c_0_13]) ).

cnf(c_0_16,plain,
    ( X1 = esk7_3(X1,X2,X3)
    | empty_carrier(X2)
    | empty_carrier(X3)
    | ~ in(X1,a_2_1_yellow19(X2,X3))
    | ~ one_sorted_str(X2)
    | ~ net_str(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_17,negated_conjecture,
    ( is_eventually_in(esk35_0,esk36_0,esk7_3(X1,esk35_0,esk36_0))
    | ~ in(X1,filter_of_net_str(esk35_0,esk36_0)) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_11]),c_0_15])]),c_0_12]),c_0_13]) ).

cnf(c_0_18,negated_conjecture,
    ( is_eventually_in(esk35_0,esk36_0,esk37_0)
    | in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_19,negated_conjecture,
    ( esk7_3(X1,esk35_0,esk36_0) = X1
    | ~ in(X1,filter_of_net_str(esk35_0,esk36_0)) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_10]),c_0_11]),c_0_15])]),c_0_12]),c_0_13]) ).

cnf(c_0_20,plain,
    ( element(esk7_3(X1,X2,X3),powerset(the_carrier(X2)))
    | empty_carrier(X2)
    | empty_carrier(X3)
    | ~ in(X1,a_2_1_yellow19(X2,X3))
    | ~ one_sorted_str(X2)
    | ~ net_str(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_21,negated_conjecture,
    ( is_eventually_in(esk35_0,esk36_0,esk7_3(esk37_0,esk35_0,esk36_0))
    | is_eventually_in(esk35_0,esk36_0,esk37_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    ( esk7_3(esk37_0,esk35_0,esk36_0) = esk37_0
    | is_eventually_in(esk35_0,esk36_0,esk37_0) ),
    inference(spm,[status(thm)],[c_0_19,c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    ( element(esk7_3(X1,esk35_0,esk36_0),powerset(the_carrier(esk35_0)))
    | ~ in(X1,filter_of_net_str(esk35_0,esk36_0)) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_10]),c_0_11]),c_0_15])]),c_0_12]),c_0_13]) ).

cnf(c_0_24,negated_conjecture,
    ( element(esk37_0,powerset(the_carrier(esk35_0)))
    | in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_25,negated_conjecture,
    ( ~ in(esk37_0,filter_of_net_str(esk35_0,esk36_0))
    | ~ is_eventually_in(esk35_0,esk36_0,esk37_0)
    | ~ element(esk37_0,powerset(the_carrier(esk35_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_26,negated_conjecture,
    is_eventually_in(esk35_0,esk36_0,esk37_0),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_27,negated_conjecture,
    ( element(esk7_3(esk37_0,esk35_0,esk36_0),powerset(the_carrier(esk35_0)))
    | element(esk37_0,powerset(the_carrier(esk35_0))) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_28,negated_conjecture,
    ( esk7_3(esk37_0,esk35_0,esk36_0) = esk37_0
    | element(esk37_0,powerset(the_carrier(esk35_0))) ),
    inference(spm,[status(thm)],[c_0_19,c_0_24]) ).

cnf(c_0_29,plain,
    ( in(X3,a_2_1_yellow19(X2,X4))
    | empty_carrier(X2)
    | empty_carrier(X4)
    | ~ element(X1,powerset(the_carrier(X2)))
    | X3 != X1
    | ~ is_eventually_in(X2,X4,X1)
    | ~ one_sorted_str(X2)
    | ~ net_str(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_30,negated_conjecture,
    ( ~ element(esk37_0,powerset(the_carrier(esk35_0)))
    | ~ in(esk37_0,filter_of_net_str(esk35_0,esk36_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).

cnf(c_0_31,negated_conjecture,
    element(esk37_0,powerset(the_carrier(esk35_0))),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_32,plain,
    ( empty_carrier(X1)
    | empty_carrier(X2)
    | in(X3,a_2_1_yellow19(X2,X1))
    | ~ is_eventually_in(X2,X1,X3)
    | ~ net_str(X1,X2)
    | ~ one_sorted_str(X2)
    | ~ element(X3,powerset(the_carrier(X2))) ),
    inference(er,[status(thm)],[c_0_29]) ).

cnf(c_0_33,negated_conjecture,
    ~ in(esk37_0,filter_of_net_str(esk35_0,esk36_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).

cnf(c_0_34,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[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_32,c_0_26]),c_0_15]),c_0_10]),c_0_11]),c_0_31])]),c_0_13]),c_0_12]),c_0_33]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU391+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n006.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Wed Aug 23 19:52:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.55  start to proof: theBenchmark
% 0.21/0.63  % Version  : CSE_E---1.5
% 0.21/0.63  % Problem  : theBenchmark.p
% 0.21/0.63  % Proof found
% 0.21/0.63  % SZS status Theorem for theBenchmark.p
% 0.21/0.63  % SZS output start Proof
% See solution above
% 0.21/0.64  % Total time : 0.069000 s
% 0.21/0.64  % SZS output end Proof
% 0.21/0.64  % Total time : 0.075000 s
%------------------------------------------------------------------------------