TSTP Solution File: SEU171+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU171+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n029.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 16:23:03 EDT 2023

% Result   : Theorem 0.19s 0.67s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   55
% Syntax   : Number of formulae    :   86 (  14 unt;  48 typ;   0 def)
%            Number of atoms       :  118 (  26 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  128 (  48   ~;  40   |;  18   &)
%                                         (   8 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   86 (  42   >;  44   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   41 (  41 usr;   6 con; 0-4 aty)
%            Number of variables   :   55 (   0 sgn;  38   !;   1   ?;   0   :)

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

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

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

tff(decl_25,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_26,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

tff(decl_29,type,
    empty_set: $i ).

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

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

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

tff(decl_33,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

tff(decl_35,type,
    union: $i > $i ).

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

tff(decl_37,type,
    subset_complement: ( $i * $i ) > $i ).

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

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

tff(decl_40,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_41,type,
    esk2_1: $i > $i ).

tff(decl_42,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_43,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_44,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk6_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_46,type,
    esk7_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_47,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_48,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_49,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_51,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_53,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk15_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_56,type,
    esk17_1: $i > $i ).

tff(decl_57,type,
    esk18_1: $i > $i ).

tff(decl_58,type,
    esk19_0: $i ).

tff(decl_59,type,
    esk20_1: $i > $i ).

tff(decl_60,type,
    esk21_0: $i ).

tff(decl_61,type,
    esk22_1: $i > $i ).

tff(decl_62,type,
    esk23_2: ( $i * $i ) > $i ).

tff(decl_63,type,
    esk24_2: ( $i * $i ) > $i ).

tff(decl_64,type,
    esk25_2: ( $i * $i ) > $i ).

tff(decl_65,type,
    esk26_0: $i ).

tff(decl_66,type,
    esk27_0: $i ).

tff(decl_67,type,
    esk28_0: $i ).

tff(decl_68,type,
    esk29_1: $i > $i ).

tff(decl_69,type,
    esk30_2: ( $i * $i ) > $i ).

fof(d2_subset_1,axiom,
    ! [X1,X2] :
      ( ( ~ empty(X1)
       => ( element(X2,X1)
        <=> in(X2,X1) ) )
      & ( empty(X1)
       => ( element(X2,X1)
        <=> empty(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).

fof(t50_subset_1,conjecture,
    ! [X1] :
      ( X1 != empty_set
     => ! [X2] :
          ( element(X2,powerset(X1))
         => ! [X3] :
              ( element(X3,X1)
             => ( ~ in(X3,X2)
               => in(X3,subset_complement(X1,X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).

fof(t6_boole,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(rc1_xboole_0,axiom,
    ? [X1] : empty(X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(d4_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_difference(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & ~ in(X4,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).

fof(t8_boole,axiom,
    ! [X1,X2] :
      ~ ( empty(X1)
        & X1 != X2
        & empty(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

fof(d5_subset_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => subset_complement(X1,X2) = set_difference(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).

fof(c_0_7,plain,
    ! [X1,X2] :
      ( ( ~ empty(X1)
       => ( element(X2,X1)
        <=> in(X2,X1) ) )
      & ( empty(X1)
       => ( element(X2,X1)
        <=> empty(X2) ) ) ),
    inference(fof_simplification,[status(thm)],[d2_subset_1]) ).

fof(c_0_8,negated_conjecture,
    ~ ! [X1] :
        ( X1 != empty_set
       => ! [X2] :
            ( element(X2,powerset(X1))
           => ! [X3] :
                ( element(X3,X1)
               => ( ~ in(X3,X2)
                 => in(X3,subset_complement(X1,X2)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t50_subset_1])]) ).

fof(c_0_9,plain,
    ! [X266] :
      ( ~ empty(X266)
      | X266 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).

fof(c_0_10,plain,
    empty(esk19_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).

fof(c_0_11,plain,
    ! [X1,X2,X3] :
      ( X3 = set_difference(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & ~ in(X4,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).

fof(c_0_12,plain,
    ! [X275,X276] :
      ( ~ empty(X275)
      | X275 = X276
      | ~ empty(X276) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).

fof(c_0_13,plain,
    ! [X37,X38] :
      ( ( ~ element(X38,X37)
        | in(X38,X37)
        | empty(X37) )
      & ( ~ in(X38,X37)
        | element(X38,X37)
        | empty(X37) )
      & ( ~ element(X38,X37)
        | empty(X38)
        | ~ empty(X37) )
      & ( ~ empty(X38)
        | element(X38,X37)
        | ~ empty(X37) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_14,negated_conjecture,
    ( esk26_0 != empty_set
    & element(esk27_0,powerset(esk26_0))
    & element(esk28_0,esk26_0)
    & ~ in(esk28_0,esk27_0)
    & ~ in(esk28_0,subset_complement(esk26_0,esk27_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

cnf(c_0_15,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,plain,
    empty(esk19_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_17,plain,
    ! [X109,X110] :
      ( ~ element(X110,powerset(X109))
      | subset_complement(X109,X110) = set_difference(X109,X110) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).

fof(c_0_18,plain,
    ! [X100,X101,X102,X103,X104,X105,X106,X107] :
      ( ( in(X103,X100)
        | ~ in(X103,X102)
        | X102 != set_difference(X100,X101) )
      & ( ~ in(X103,X101)
        | ~ in(X103,X102)
        | X102 != set_difference(X100,X101) )
      & ( ~ in(X104,X100)
        | in(X104,X101)
        | in(X104,X102)
        | X102 != set_difference(X100,X101) )
      & ( ~ in(esk16_3(X105,X106,X107),X107)
        | ~ in(esk16_3(X105,X106,X107),X105)
        | in(esk16_3(X105,X106,X107),X106)
        | X107 = set_difference(X105,X106) )
      & ( in(esk16_3(X105,X106,X107),X105)
        | in(esk16_3(X105,X106,X107),X107)
        | X107 = set_difference(X105,X106) )
      & ( ~ in(esk16_3(X105,X106,X107),X106)
        | in(esk16_3(X105,X106,X107),X107)
        | X107 = set_difference(X105,X106) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])]) ).

cnf(c_0_19,plain,
    ( X1 = X2
    | ~ empty(X1)
    | ~ empty(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,plain,
    ( in(X1,X2)
    | empty(X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,negated_conjecture,
    element(esk28_0,esk26_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,negated_conjecture,
    esk26_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_23,plain,
    empty_set = esk19_0,
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_24,plain,
    ( subset_complement(X2,X1) = set_difference(X2,X1)
    | ~ element(X1,powerset(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,negated_conjecture,
    element(esk27_0,powerset(esk26_0)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_26,plain,
    ( in(X1,X3)
    | in(X1,X4)
    | ~ in(X1,X2)
    | X4 != set_difference(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_27,plain,
    ( esk19_0 = X1
    | ~ empty(X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_16]) ).

cnf(c_0_28,negated_conjecture,
    ( empty(esk26_0)
    | in(esk28_0,esk26_0) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_29,negated_conjecture,
    esk26_0 != esk19_0,
    inference(rw,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_30,negated_conjecture,
    ~ in(esk28_0,subset_complement(esk26_0,esk27_0)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_31,negated_conjecture,
    subset_complement(esk26_0,esk27_0) = set_difference(esk26_0,esk27_0),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_32,plain,
    ( in(X1,set_difference(X2,X3))
    | in(X1,X3)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[c_0_26]) ).

cnf(c_0_33,negated_conjecture,
    in(esk28_0,esk26_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_34,negated_conjecture,
    ~ in(esk28_0,set_difference(esk26_0,esk27_0)),
    inference(rw,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    ( in(esk28_0,set_difference(esk26_0,X1))
    | in(esk28_0,X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_36,negated_conjecture,
    ~ in(esk28_0,esk27_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_37,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU171+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n029.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   : Wed Aug 23 14:08:07 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.67  % Version  : CSE_E---1.5
% 0.19/0.67  % Problem  : theBenchmark.p
% 0.19/0.67  % Proof found
% 0.19/0.67  % SZS status Theorem for theBenchmark.p
% 0.19/0.67  % SZS output start Proof
% See solution above
% 0.19/0.68  % Total time : 0.107000 s
% 0.19/0.68  % SZS output end Proof
% 0.19/0.68  % Total time : 0.110000 s
%------------------------------------------------------------------------------