TSTP Solution File: SEU169+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU169+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 : n024.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 16:23:02 EDT 2023

% Result   : Theorem 0.35s 0.71s
% Output   : CNFRefutation 0.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   51
% Syntax   : Number of formulae    :   71 (  10 unt;  46 typ;   0 def)
%            Number of atoms       :   81 (   6 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :   87 (  31   ~;  28   |;  12   &)
%                                         (   7 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   83 (  40   >;  43   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   39 (  39 usr;   6 con; 0-4 aty)
%            Number of variables   :   44 (   1 sgn;  32   !;   0   ?;   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,
    disjoint: ( $i * $i ) > $o ).

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

tff(decl_39,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_40,type,
    esk2_1: $i > $i ).

tff(decl_41,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_42,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_43,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_44,type,
    esk6_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk7_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_46,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_47,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_48,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_49,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_50,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk15_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_55,type,
    esk17_1: $i > $i ).

tff(decl_56,type,
    esk18_0: $i ).

tff(decl_57,type,
    esk19_0: $i ).

tff(decl_58,type,
    esk20_0: $i ).

tff(decl_59,type,
    esk21_1: $i > $i ).

tff(decl_60,type,
    esk22_0: $i ).

tff(decl_61,type,
    esk23_0: $i ).

tff(decl_62,type,
    esk24_1: $i > $i ).

tff(decl_63,type,
    esk25_2: ( $i * $i ) > $i ).

tff(decl_64,type,
    esk26_2: ( $i * $i ) > $i ).

tff(decl_65,type,
    esk27_2: ( $i * $i ) > $i ).

tff(decl_66,type,
    esk28_1: $i > $i ).

tff(decl_67,type,
    esk29_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(l3_subset_1,conjecture,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => ! [X3] :
          ( in(X3,X2)
         => in(X3,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).

fof(fc1_subset_1,axiom,
    ! [X1] : ~ empty(powerset(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).

fof(d1_zfmisc_1,axiom,
    ! [X1,X2] :
      ( X2 = powerset(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> subset(X3,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(c_0_5,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_6,negated_conjecture,
    ~ ! [X1,X2] :
        ( element(X2,powerset(X1))
       => ! [X3] :
            ( in(X3,X2)
           => in(X3,X1) ) ),
    inference(assume_negation,[status(cth)],[l3_subset_1]) ).

fof(c_0_7,plain,
    ! [X1] : ~ empty(powerset(X1)),
    inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).

fof(c_0_8,plain,
    ! [X30,X31,X32,X33,X34,X35] :
      ( ( ~ in(X32,X31)
        | subset(X32,X30)
        | X31 != powerset(X30) )
      & ( ~ subset(X33,X30)
        | in(X33,X31)
        | X31 != powerset(X30) )
      & ( ~ in(esk3_2(X34,X35),X35)
        | ~ subset(esk3_2(X34,X35),X34)
        | X35 = powerset(X34) )
      & ( in(esk3_2(X34,X35),X35)
        | subset(esk3_2(X34,X35),X34)
        | X35 = powerset(X34) ) ),
    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)],[d1_zfmisc_1])])])])])]) ).

fof(c_0_9,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_5])])]) ).

fof(c_0_10,negated_conjecture,
    ( element(esk19_0,powerset(esk18_0))
    & in(esk20_0,esk19_0)
    & ~ in(esk20_0,esk18_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

fof(c_0_11,plain,
    ! [X117] : ~ empty(powerset(X117)),
    inference(variable_rename,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    ( subset(X1,X3)
    | ~ in(X1,X2)
    | X2 != powerset(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    ( in(X1,X2)
    | empty(X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,negated_conjecture,
    element(esk19_0,powerset(esk18_0)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,plain,
    ~ empty(powerset(X1)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_16,plain,
    ! [X74,X75,X76,X77,X78] :
      ( ( ~ subset(X74,X75)
        | ~ in(X76,X74)
        | in(X76,X75) )
      & ( in(esk11_2(X77,X78),X77)
        | subset(X77,X78) )
      & ( ~ in(esk11_2(X77,X78),X78)
        | subset(X77,X78) ) ),
    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)],[d3_tarski])])])])])]) ).

cnf(c_0_17,plain,
    ( subset(X1,X2)
    | ~ in(X1,powerset(X2)) ),
    inference(er,[status(thm)],[c_0_12]) ).

cnf(c_0_18,negated_conjecture,
    in(esk19_0,powerset(esk18_0)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).

cnf(c_0_19,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_20,negated_conjecture,
    subset(esk19_0,esk18_0),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    ~ in(esk20_0,esk18_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_22,negated_conjecture,
    ( in(X1,esk18_0)
    | ~ in(X1,esk19_0) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,negated_conjecture,
    in(esk20_0,esk19_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_24,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem    : SEU169+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.07/0.35  % Computer : n024.cluster.edu
% 0.07/0.35  % Model    : x86_64 x86_64
% 0.07/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35  % Memory   : 8042.1875MB
% 0.07/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.35  % CPULimit   : 300
% 0.07/0.35  % WCLimit    : 300
% 0.07/0.35  % DateTime   : Wed Aug 23 14:26:09 EDT 2023
% 0.11/0.36  % CPUTime  : 
% 0.35/0.68  start to proof: theBenchmark
% 0.35/0.71  % Version  : CSE_E---1.5
% 0.35/0.71  % Problem  : theBenchmark.p
% 0.35/0.71  % Proof found
% 0.35/0.71  % SZS status Theorem for theBenchmark.p
% 0.35/0.71  % SZS output start Proof
% See solution above
% 0.40/0.72  % Total time : 0.030000 s
% 0.40/0.72  % SZS output end Proof
% 0.40/0.72  % Total time : 0.032000 s
%------------------------------------------------------------------------------