TSTP Solution File: SET984+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n020.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 14:36:31 EDT 2023

% Result   : Theorem 0.21s 0.62s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   52 (  17 unt;  11 typ;   0 def)
%            Number of atoms       :  102 (  80 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   84 (  23   ~;  48   |;   8   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   82 (  12 sgn;  40   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    set_intersection2: ( $i * $i ) > $i ).

tff(decl_23,type,
    empty_set: $i ).

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

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

tff(decl_26,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff(decl_27,type,
    esk1_0: $i ).

tff(decl_28,type,
    esk2_0: $i ).

tff(decl_29,type,
    esk3_0: $i ).

tff(decl_30,type,
    esk4_0: $i ).

tff(decl_31,type,
    esk5_0: $i ).

tff(decl_32,type,
    esk6_0: $i ).

fof(t138_zfmisc_1,conjecture,
    ! [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/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).

fof(t134_zfmisc_1,axiom,
    ! [X1,X2,X3,X4] :
      ( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
     => ( X1 = empty_set
        | X2 = empty_set
        | ( X1 = X3
          & X2 = X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).

fof(t123_zfmisc_1,axiom,
    ! [X1,X2,X3,X4] : cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).

fof(t28_xboole_1,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
     => set_intersection2(X1,X2) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).

fof(t17_xboole_1,axiom,
    ! [X1,X2] : subset(set_intersection2(X1,X2),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).

fof(commutativity_k3_xboole_0,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(t113_zfmisc_1,axiom,
    ! [X1,X2] :
      ( cartesian_product2(X1,X2) = empty_set
    <=> ( X1 = empty_set
        | X2 = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).

fof(c_0_7,negated_conjecture,
    ~ ! [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) ) ) ),
    inference(assume_negation,[status(cth)],[t138_zfmisc_1]) ).

fof(c_0_8,plain,
    ! [X17,X18,X19,X20] :
      ( ( X17 = X19
        | X17 = empty_set
        | X18 = empty_set
        | cartesian_product2(X17,X18) != cartesian_product2(X19,X20) )
      & ( X18 = X20
        | X17 = empty_set
        | X18 = empty_set
        | cartesian_product2(X17,X18) != cartesian_product2(X19,X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t134_zfmisc_1])])]) ).

fof(c_0_9,plain,
    ! [X13,X14,X15,X16] : cartesian_product2(set_intersection2(X13,X14),set_intersection2(X15,X16)) = set_intersection2(cartesian_product2(X13,X15),cartesian_product2(X14,X16)),
    inference(variable_rename,[status(thm)],[t123_zfmisc_1]) ).

fof(c_0_10,plain,
    ! [X27,X28] :
      ( ~ subset(X27,X28)
      | set_intersection2(X27,X28) = X27 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).

fof(c_0_11,negated_conjecture,
    ( subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
    & cartesian_product2(esk3_0,esk4_0) != empty_set
    & ( ~ subset(esk3_0,esk5_0)
      | ~ subset(esk4_0,esk6_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_12,plain,
    ( X1 = X2
    | X3 = empty_set
    | X1 = empty_set
    | cartesian_product2(X3,X1) != cartesian_product2(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( set_intersection2(X1,X2) = X1
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_16,plain,
    ! [X25,X26] : subset(set_intersection2(X25,X26),X25),
    inference(variable_rename,[status(thm)],[t17_xboole_1]) ).

fof(c_0_17,plain,
    ! [X5,X6] : set_intersection2(X5,X6) = set_intersection2(X6,X5),
    inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).

cnf(c_0_18,plain,
    ( X1 = set_intersection2(X2,X3)
    | X1 = empty_set
    | X4 = empty_set
    | cartesian_product2(X4,X1) != set_intersection2(cartesian_product2(X5,X2),cartesian_product2(X6,X3)) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    set_intersection2(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) = cartesian_product2(esk3_0,esk4_0),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,plain,
    ( X1 = X2
    | X1 = empty_set
    | X3 = empty_set
    | cartesian_product2(X1,X3) != cartesian_product2(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_21,plain,
    subset(set_intersection2(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    ( X1 = set_intersection2(esk4_0,esk6_0)
    | X2 = empty_set
    | X1 = empty_set
    | cartesian_product2(X2,X1) != cartesian_product2(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,plain,
    ( X1 = set_intersection2(X2,X3)
    | X1 = empty_set
    | X4 = empty_set
    | cartesian_product2(X1,X4) != set_intersection2(cartesian_product2(X2,X5),cartesian_product2(X3,X6)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_13]) ).

cnf(c_0_25,plain,
    subset(set_intersection2(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,negated_conjecture,
    ( set_intersection2(esk4_0,esk6_0) = esk4_0
    | esk4_0 = empty_set
    | esk3_0 = empty_set ),
    inference(er,[status(thm)],[c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    ( X1 = set_intersection2(esk3_0,esk5_0)
    | X2 = empty_set
    | X1 = empty_set
    | cartesian_product2(X1,X2) != cartesian_product2(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[c_0_24,c_0_19]) ).

cnf(c_0_28,negated_conjecture,
    ( ~ subset(esk3_0,esk5_0)
    | ~ subset(esk4_0,esk6_0) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_29,negated_conjecture,
    ( esk3_0 = empty_set
    | esk4_0 = empty_set
    | subset(esk4_0,esk6_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

fof(c_0_30,plain,
    ! [X11,X12] :
      ( ( cartesian_product2(X11,X12) != empty_set
        | X11 = empty_set
        | X12 = empty_set )
      & ( X11 != empty_set
        | cartesian_product2(X11,X12) = empty_set )
      & ( X12 != empty_set
        | cartesian_product2(X11,X12) = empty_set ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t113_zfmisc_1])])]) ).

cnf(c_0_31,negated_conjecture,
    ( set_intersection2(esk3_0,esk5_0) = esk3_0
    | esk3_0 = empty_set
    | esk4_0 = empty_set ),
    inference(er,[status(thm)],[c_0_27]) ).

cnf(c_0_32,negated_conjecture,
    ( esk4_0 = empty_set
    | esk3_0 = empty_set
    | ~ subset(esk3_0,esk5_0) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,plain,
    ( cartesian_product2(X2,X1) = empty_set
    | X1 != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_34,negated_conjecture,
    cartesian_product2(esk3_0,esk4_0) != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_35,negated_conjecture,
    ( esk4_0 = empty_set
    | esk3_0 = empty_set ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_31]),c_0_32]) ).

cnf(c_0_36,plain,
    cartesian_product2(X1,empty_set) = empty_set,
    inference(er,[status(thm)],[c_0_33]) ).

cnf(c_0_37,plain,
    ( cartesian_product2(X1,X2) = empty_set
    | X1 != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_38,negated_conjecture,
    esk3_0 = empty_set,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).

cnf(c_0_39,plain,
    cartesian_product2(empty_set,X1) = empty_set,
    inference(er,[status(thm)],[c_0_37]) ).

cnf(c_0_40,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_38]),c_0_39])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n020.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   : Sat Aug 26 11:05:45 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.21/0.62  % Version  : CSE_E---1.5
% 0.21/0.62  % Problem  : theBenchmark.p
% 0.21/0.62  % Proof found
% 0.21/0.62  % SZS status Theorem for theBenchmark.p
% 0.21/0.62  % SZS output start Proof
% See solution above
% 0.21/0.62  % Total time : 0.025000 s
% 0.21/0.62  % SZS output end Proof
% 0.21/0.62  % Total time : 0.027000 s
%------------------------------------------------------------------------------