%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET954+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 : 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 14:36:25 EDT 2023

% Result   : Theorem 0.18s 0.57s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   33 (  10 unt;  12 typ;   0 def)
%            Number of atoms       :   40 (   3 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   35 (  16   ~;  12   |;   4   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   46 (   7 sgn;  20   !;   0   ?;   0   :)

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

tff(decl_23,type,
    unordered_pair: ( $i * $i ) > $i ).

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

tff(decl_25,type,
    singleton: $i > $i ).

tff(decl_26,type,
    empty: $i > $o ).

tff(decl_27,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff(decl_28,type,
    esk1_0: $i ).

tff(decl_29,type,
    esk2_0: $i ).

tff(decl_30,type,
    esk3_0: $i ).

tff(decl_31,type,
    esk4_0: $i ).

tff(decl_32,type,
    esk5_0: $i ).

tff(decl_33,type,
    esk6_0: $i ).

fof(t107_zfmisc_1,conjecture,
    ! [X1,X2,X3,X4] :
      ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
     => in(ordered_pair(X2,X1),cartesian_product2(X4,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_zfmisc_1) ).

fof(l55_zfmisc_1,axiom,
    ! [X1,X2,X3,X4] :
      ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
    <=> ( in(X1,X3)
        & in(X2,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).

fof(d5_tarski,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
       => in(ordered_pair(X2,X1),cartesian_product2(X4,X3)) ),
    inference(assume_negation,[status(cth)],[t107_zfmisc_1]) ).

fof(c_0_4,plain,
    ! [X13,X14,X15,X16] :
      ( ( in(X13,X15)
        | ~ in(ordered_pair(X13,X14),cartesian_product2(X15,X16)) )
      & ( in(X14,X16)
        | ~ in(ordered_pair(X13,X14),cartesian_product2(X15,X16)) )
      & ( ~ in(X13,X15)
        | ~ in(X14,X16)
        | in(ordered_pair(X13,X14),cartesian_product2(X15,X16)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).

fof(c_0_5,plain,
    ! [X9,X10] : ordered_pair(X9,X10) = unordered_pair(unordered_pair(X9,X10),singleton(X9)),
    inference(variable_rename,[status(thm)],[d5_tarski]) ).

fof(c_0_6,negated_conjecture,
    ( in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
    & ~ in(ordered_pair(esk4_0,esk3_0),cartesian_product2(esk6_0,esk5_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_7,plain,
    ( in(X1,X2)
    | ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( in(X1,X2)
    | ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_11,negated_conjecture,
    ~ in(ordered_pair(esk4_0,esk3_0),cartesian_product2(esk6_0,esk5_0)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,plain,
    ( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
    | ~ in(X1,X2)
    | ~ in(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_13,plain,
    ( in(X1,X2)
    | ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)),
    inference(rw,[status(thm)],[c_0_9,c_0_8]) ).

cnf(c_0_15,plain,
    ( in(X1,X2)
    | ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
    inference(rw,[status(thm)],[c_0_10,c_0_8]) ).

cnf(c_0_16,negated_conjecture,
    ~ in(unordered_pair(unordered_pair(esk4_0,esk3_0),singleton(esk4_0)),cartesian_product2(esk6_0,esk5_0)),
    inference(rw,[status(thm)],[c_0_11,c_0_8]) ).

cnf(c_0_17,plain,
    ( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4))
    | ~ in(X3,X4)
    | ~ in(X1,X2) ),
    inference(rw,[status(thm)],[c_0_12,c_0_8]) ).

cnf(c_0_18,negated_conjecture,
    in(esk3_0,esk5_0),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_19,negated_conjecture,
    in(esk4_0,esk6_0),
    inference(spm,[status(thm)],[c_0_15,c_0_14]) ).

cnf(c_0_20,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET954+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
% 0.13/0.33  % 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   : Sat Aug 26 08:31:40 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.18/0.55  start to proof: theBenchmark
% 0.18/0.57  % Version  : CSE_E---1.5
% 0.18/0.57  % Problem  : theBenchmark.p
% 0.18/0.57  % Proof found
% 0.18/0.57  % SZS status Theorem for theBenchmark.p
% 0.18/0.57  % SZS output start Proof
% See solution above
% 0.18/0.57  % Total time : 0.007000 s
% 0.18/0.57  % SZS output end Proof
% 0.18/0.57  % Total time : 0.010000 s
%------------------------------------------------------------------------------