TSTP Solution File: SET968+1 by CSE

TSTP Solution File: SET968+1 by CSE_E---1.5

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET968+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 : n032.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 14:36:28 EDT 2023

% Result   : Theorem 0.14s 0.47s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   28 (  17 unt;   9 typ;   0 def)
%            Number of atoms       :   21 (  20 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   5   ~;   0   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   40 (   0 sgn;  24   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    set_union2: ( $i * $i ) > $i ).

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

tff(decl_24,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff(decl_25,type,
    esk1_0: $i ).

tff(decl_26,type,
    esk2_0: $i ).

tff(decl_27,type,
    esk3_0: $i ).

tff(decl_28,type,
    esk4_0: $i ).

tff(decl_29,type,
    esk5_0: $i ).

tff(decl_30,type,
    esk6_0: $i ).

fof(t121_zfmisc_1,conjecture,
    ! [X1,X2,X3,X4] : cartesian_product2(set_union2(X1,X2),set_union2(X3,X4)) = set_union2(set_union2(set_union2(cartesian_product2(X1,X3),cartesian_product2(X1,X4)),cartesian_product2(X2,X3)),cartesian_product2(X2,X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).

fof(commutativity_k2_xboole_0,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(t4_xboole_1,axiom,
    ! [X1,X2,X3] : set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).

fof(t120_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
      & cartesian_product2(X3,set_union2(X1,X2)) = set_union2(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2,X3,X4] : cartesian_product2(set_union2(X1,X2),set_union2(X3,X4)) = set_union2(set_union2(set_union2(cartesian_product2(X1,X3),cartesian_product2(X1,X4)),cartesian_product2(X2,X3)),cartesian_product2(X2,X4)),
    inference(assume_negation,[status(cth)],[t121_zfmisc_1]) ).

fof(c_0_5,negated_conjecture,
    cartesian_product2(set_union2(esk3_0,esk4_0),set_union2(esk5_0,esk6_0)) != set_union2(set_union2(set_union2(cartesian_product2(esk3_0,esk5_0),cartesian_product2(esk3_0,esk6_0)),cartesian_product2(esk4_0,esk5_0)),cartesian_product2(esk4_0,esk6_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

fof(c_0_6,plain,
    ! [X5,X6] : set_union2(X5,X6) = set_union2(X6,X5),
    inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).

cnf(c_0_7,negated_conjecture,
    cartesian_product2(set_union2(esk3_0,esk4_0),set_union2(esk5_0,esk6_0)) != set_union2(set_union2(set_union2(cartesian_product2(esk3_0,esk5_0),cartesian_product2(esk3_0,esk6_0)),cartesian_product2(esk4_0,esk5_0)),cartesian_product2(esk4_0,esk6_0)),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_9,plain,
    ! [X21,X22,X23] : set_union2(set_union2(X21,X22),X23) = set_union2(X21,set_union2(X22,X23)),
    inference(variable_rename,[status(thm)],[t4_xboole_1]) ).

cnf(c_0_10,negated_conjecture,
    cartesian_product2(set_union2(esk3_0,esk4_0),set_union2(esk5_0,esk6_0)) != set_union2(set_union2(cartesian_product2(esk4_0,esk5_0),set_union2(cartesian_product2(esk3_0,esk5_0),cartesian_product2(esk3_0,esk6_0))),cartesian_product2(esk4_0,esk6_0)),
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,plain,
    set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_12,plain,
    ! [X14,X15,X16] :
      ( cartesian_product2(set_union2(X14,X15),X16) = set_union2(cartesian_product2(X14,X16),cartesian_product2(X15,X16))
      & cartesian_product2(X16,set_union2(X14,X15)) = set_union2(cartesian_product2(X16,X14),cartesian_product2(X16,X15)) ),
    inference(variable_rename,[status(thm)],[t120_zfmisc_1]) ).

cnf(c_0_13,negated_conjecture,
    cartesian_product2(set_union2(esk3_0,esk4_0),set_union2(esk5_0,esk6_0)) != set_union2(cartesian_product2(esk4_0,esk5_0),set_union2(cartesian_product2(esk3_0,esk5_0),set_union2(cartesian_product2(esk3_0,esk6_0),cartesian_product2(esk4_0,esk6_0)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).

cnf(c_0_14,plain,
    cartesian_product2(X1,set_union2(X2,X3)) = set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_15,plain,
    cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_16,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    c_0_8 ).

cnf(c_0_17,plain,
    set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
    c_0_11 ).

cnf(c_0_18,negated_conjecture,
    $false,
    inference(ar,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_15]),c_0_11]),c_0_16,c_0_17]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SET968+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.10  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit   : 300
% 0.10/0.29  % WCLimit    : 300
% 0.10/0.29  % DateTime   : Sat Aug 26 15:06:14 EDT 2023
% 0.10/0.29  % CPUTime  : 
% 0.14/0.46  start to proof: theBenchmark
% 0.14/0.47  % Version  : CSE_E---1.5
% 0.14/0.47  % Problem  : theBenchmark.p
% 0.14/0.47  % Proof found
% 0.14/0.47  % SZS status Theorem for theBenchmark.p
% 0.14/0.47  % SZS output start Proof
% See solution above
% 0.14/0.48  % Total time : 0.004000 s
% 0.14/0.48  % SZS output end Proof
% 0.14/0.48  % Total time : 0.006000 s
%------------------------------------------------------------------------------