TSTP Solution File: SET985+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET985+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n013.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 14:36:32 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   33 (   9 unt;  10 typ;   0 def)
%            Number of atoms       :   58 (  24 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   50 (  15   ~;  23   |;   6   &)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :   33 (   3 sgn;  22   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    empty_set: $i ).

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

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

tff(decl_25,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff(decl_26,type,
    esk1_0: $i ).

tff(decl_27,type,
    esk2_0: $i ).

tff(decl_28,type,
    esk3_0: $i ).

tff(decl_29,type,
    esk4_0: $i ).

tff(decl_30,type,
    esk5_0: $i ).

tff(decl_31,type,
    esk6_0: $i ).

fof(t139_zfmisc_1,conjecture,
    ! [X1] :
      ( ~ empty(X1)
     => ! [X2,X3,X4] :
          ( ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
            | subset(cartesian_product2(X2,X1),cartesian_product2(X4,X3)) )
         => subset(X2,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_zfmisc_1) ).

fof(t138_zfmisc_1,axiom,
    ! [X1,X2,X3,X4] :
      ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
     => ( cartesian_product2(X1,X2) = empty_set
        | ( subset(X1,X3)
          & subset(X2,X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).

fof(t113_zfmisc_1,axiom,
    ! [X1,X2] :
      ( cartesian_product2(X1,X2) = empty_set
    <=> ( X1 = empty_set
        | X2 = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).

fof(t2_xboole_1,axiom,
    ! [X1] : subset(empty_set,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).

fof(fc1_xboole_0,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1] :
        ( ~ empty(X1)
       => ! [X2,X3,X4] :
            ( ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
              | subset(cartesian_product2(X2,X1),cartesian_product2(X4,X3)) )
           => subset(X2,X4) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t139_zfmisc_1])]) ).

fof(c_0_6,plain,
    ! [X10,X11,X12,X13] :
      ( ( subset(X10,X12)
        | cartesian_product2(X10,X11) = empty_set
        | ~ subset(cartesian_product2(X10,X11),cartesian_product2(X12,X13)) )
      & ( subset(X11,X13)
        | cartesian_product2(X10,X11) = empty_set
        | ~ subset(cartesian_product2(X10,X11),cartesian_product2(X12,X13)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t138_zfmisc_1])])]) ).

fof(c_0_7,negated_conjecture,
    ( ~ empty(esk3_0)
    & ( subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
      | subset(cartesian_product2(esk4_0,esk3_0),cartesian_product2(esk6_0,esk5_0)) )
    & ~ subset(esk4_0,esk6_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

cnf(c_0_8,plain,
    ( subset(X1,X2)
    | cartesian_product2(X1,X3) = empty_set
    | ~ subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,negated_conjecture,
    ( subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
    | subset(cartesian_product2(esk4_0,esk3_0),cartesian_product2(esk6_0,esk5_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    ~ subset(esk4_0,esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X8,X9] :
      ( ( cartesian_product2(X8,X9) != empty_set
        | X8 = empty_set
        | X9 = empty_set )
      & ( X8 != empty_set
        | cartesian_product2(X8,X9) = empty_set )
      & ( X9 != empty_set
        | cartesian_product2(X8,X9) = empty_set ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t113_zfmisc_1])])]) ).

cnf(c_0_12,plain,
    ( subset(X1,X2)
    | cartesian_product2(X3,X1) = empty_set
    | ~ subset(cartesian_product2(X3,X1),cartesian_product2(X4,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_13,negated_conjecture,
    ( cartesian_product2(esk4_0,esk3_0) = empty_set
    | subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).

cnf(c_0_14,plain,
    ( X1 = empty_set
    | X2 = empty_set
    | cartesian_product2(X1,X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    ( cartesian_product2(esk4_0,esk3_0) = empty_set
    | cartesian_product2(esk3_0,esk4_0) = empty_set ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_10]) ).

fof(c_0_16,plain,
    ! [X18] : subset(empty_set,X18),
    inference(variable_rename,[status(thm)],[t2_xboole_1]) ).

cnf(c_0_17,negated_conjecture,
    ( esk4_0 = empty_set
    | esk3_0 = empty_set ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_14]) ).

cnf(c_0_18,plain,
    subset(empty_set,X1),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    ~ empty(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_20,negated_conjecture,
    esk3_0 = empty_set,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_17]),c_0_18])]) ).

cnf(c_0_21,plain,
    empty(empty_set),
    inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).

cnf(c_0_22,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET985+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n013.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   : Sat Aug 26 15:40:02 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.59  % Version  : CSE_E---1.5
% 0.19/0.59  % Problem  : theBenchmark.p
% 0.19/0.59  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.006000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.009000 s
%------------------------------------------------------------------------------