%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET962+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n026.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 14:36:27 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   42 (  11 unt;  11 typ;   0 def)
%            Number of atoms       :   68 (  20 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   62 (  25   ~;  27   |;   5   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   7   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   62 (   4 sgn;  25   !;   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_2: ( $i * $i ) > $i ).

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(t115_zfmisc_1,conjecture,
    ! [X1,X2] :
      ( cartesian_product2(X1,X1) = cartesian_product2(X2,X2)
     => X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).

fof(commutativity_k2_tarski,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(t2_tarski,axiom,
    ! [X1,X2] :
      ( ! [X3] :
          ( in(X3,X1)
        <=> in(X3,X2) )
     => X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).

fof(c_0_5,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_6,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_7,negated_conjecture,
    ~ ! [X1,X2] :
        ( cartesian_product2(X1,X1) = cartesian_product2(X2,X2)
       => X1 = X2 ),
    inference(assume_negation,[status(cth)],[t115_zfmisc_1]) ).

cnf(c_0_8,plain,
    ( in(X1,X2)
    | ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_10,plain,
    ! [X7,X8] : unordered_pair(X7,X8) = unordered_pair(X8,X7),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

cnf(c_0_11,plain,
    ( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
    | ~ in(X1,X2)
    | ~ in(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_12,negated_conjecture,
    ( cartesian_product2(esk3_0,esk3_0) = cartesian_product2(esk4_0,esk4_0)
    & esk3_0 != esk4_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_13,plain,
    ( in(X1,X2)
    | ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
    inference(rw,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_14,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,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_11,c_0_9]) ).

cnf(c_0_16,negated_conjecture,
    cartesian_product2(esk3_0,esk3_0) = cartesian_product2(esk4_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,plain,
    ( in(X1,X2)
    | ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X3)),cartesian_product2(X4,X2)) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    ( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk4_0,esk4_0))
    | ~ in(X2,esk3_0)
    | ~ in(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

fof(c_0_19,plain,
    ! [X21,X22] :
      ( ( ~ in(esk5_2(X21,X22),X21)
        | ~ in(esk5_2(X21,X22),X22)
        | X21 = X22 )
      & ( in(esk5_2(X21,X22),X21)
        | in(esk5_2(X21,X22),X22)
        | X21 = X22 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).

cnf(c_0_20,negated_conjecture,
    ( in(X1,esk4_0)
    | ~ in(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,plain,
    ( in(esk5_2(X1,X2),X1)
    | in(esk5_2(X1,X2),X2)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_22,negated_conjecture,
    ( esk3_0 = X1
    | in(esk5_2(esk3_0,X1),esk4_0)
    | in(esk5_2(esk3_0,X1),X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_23,negated_conjecture,
    esk3_0 != esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_24,negated_conjecture,
    ( in(X1,esk3_0)
    | ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),cartesian_product2(esk4_0,esk4_0)) ),
    inference(spm,[status(thm)],[c_0_13,c_0_16]) ).

cnf(c_0_25,plain,
    ( X1 = X2
    | ~ in(esk5_2(X1,X2),X1)
    | ~ in(esk5_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_26,negated_conjecture,
    in(esk5_2(esk3_0,esk4_0),esk4_0),
    inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_22]),c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    ( in(X1,esk3_0)
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X2)),cartesian_product2(esk4_0,esk4_0)) ),
    inference(spm,[status(thm)],[c_0_24,c_0_14]) ).

cnf(c_0_28,negated_conjecture,
    ~ in(esk5_2(esk3_0,esk4_0),esk3_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23]) ).

cnf(c_0_29,negated_conjecture,
    ( in(X1,esk3_0)
    | ~ in(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_27,c_0_15]) ).

cnf(c_0_30,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET962+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n026.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 09:03:33 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.60  % Total time : 0.011000 s
% 0.20/0.60  % SZS output end Proof
% 0.20/0.60  % Total time : 0.013000 s
%------------------------------------------------------------------------------