%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU167+2 : 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 : n022.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 16:23:00 EDT 2023

% Result   : Theorem 16.60s 16.72s
% Output   : CNFRefutation 16.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   43
% Syntax   : Number of formulae    :   56 (   4 unt;  40 typ;   0 def)
%            Number of atoms       :   39 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   38 (  15   ~;  12   |;   7   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   73 (  33   >;  40   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   35 (  35 usr;   7 con; 0-4 aty)
%            Number of variables   :   37 (   0 sgn;  20   !;   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,
    cartesian_product2: ( $i * $i ) > $i ).

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

tff(decl_33,type,
    union: $i > $i ).

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

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

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

tff(decl_37,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk2_1: $i > $i ).

tff(decl_39,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_40,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_41,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_42,type,
    esk6_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_43,type,
    esk7_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_44,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_46,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_47,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_48,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_49,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_51,type,
    esk15_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_53,type,
    esk17_0: $i ).

tff(decl_54,type,
    esk18_0: $i ).

tff(decl_55,type,
    esk19_0: $i ).

tff(decl_56,type,
    esk20_0: $i ).

tff(decl_57,type,
    esk21_0: $i ).

tff(decl_58,type,
    esk22_0: $i ).

tff(decl_59,type,
    esk23_2: ( $i * $i ) > $i ).

tff(decl_60,type,
    esk24_2: ( $i * $i ) > $i ).

tff(decl_61,type,
    esk25_2: ( $i * $i ) > $i ).

fof(t1_xboole_1,lemma,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X2,X3) )
     => subset(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).

fof(t118_zfmisc_1,lemma,
    ! [X1,X2,X3] :
      ( subset(X1,X2)
     => ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
        & subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).

fof(t119_zfmisc_1,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( subset(X1,X2)
        & subset(X3,X4) )
     => subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).

fof(c_0_3,lemma,
    ! [X172,X173,X174] :
      ( ~ subset(X172,X173)
      | ~ subset(X173,X174)
      | subset(X172,X174) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).

fof(c_0_4,lemma,
    ! [X157,X158,X159] :
      ( ( subset(cartesian_product2(X157,X159),cartesian_product2(X158,X159))
        | ~ subset(X157,X158) )
      & ( subset(cartesian_product2(X159,X157),cartesian_product2(X159,X158))
        | ~ subset(X157,X158) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t118_zfmisc_1])])]) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( subset(X1,X2)
          & subset(X3,X4) )
       => subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
    inference(assume_negation,[status(cth)],[t119_zfmisc_1]) ).

cnf(c_0_6,lemma,
    ( subset(X1,X3)
    | ~ subset(X1,X2)
    | ~ subset(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_7,lemma,
    ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X2))
    | ~ subset(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

fof(c_0_8,negated_conjecture,
    ( subset(esk19_0,esk20_0)
    & subset(esk21_0,esk22_0)
    & ~ subset(cartesian_product2(esk19_0,esk21_0),cartesian_product2(esk20_0,esk22_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

cnf(c_0_9,lemma,
    ( subset(X1,cartesian_product2(X2,X3))
    | ~ subset(X1,cartesian_product2(X4,X3))
    | ~ subset(X4,X2) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,lemma,
    ( subset(cartesian_product2(X1,X2),cartesian_product2(X1,X3))
    | ~ subset(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_11,negated_conjecture,
    ~ subset(cartesian_product2(esk19_0,esk21_0),cartesian_product2(esk20_0,esk22_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,lemma,
    ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
    | ~ subset(X1,X3)
    | ~ subset(X2,X4) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    subset(esk19_0,esk20_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    subset(esk21_0,esk22_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU167+2 : 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
% 0.13/0.33  % Computer : n022.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Wed Aug 23 23:48:56 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.19/0.52  start to proof: theBenchmark
% 16.60/16.72  % Version  : CSE_E---1.5
% 16.60/16.72  % Problem  : theBenchmark.p
% 16.60/16.72  % Proof found
% 16.60/16.72  % SZS status Theorem for theBenchmark.p
% 16.60/16.72  % SZS output start Proof
% See solution above
% 16.60/16.73  % Total time : 16.192000 s
% 16.60/16.73  % SZS output end Proof
% 16.60/16.73  % Total time : 16.195000 s
%------------------------------------------------------------------------------