TSTP Solution File: SET955+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET955+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n015.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  : 600s
% DateTime : Tue Jul 19 00:55:42 EDT 2022

% Result   : Theorem 0.23s 1.40s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   22 (   4 unt;   0 def)
%            Number of atoms       :   93 (  32 equ)
%            Maximal formula atoms :   28 (   4 avg)
%            Number of connectives :  109 (  38   ~;  51   |;  12   &)
%                                         (   5 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-4 aty)
%            Number of variables   :   70 (  16 sgn  37   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t108_zfmisc_1,conjecture,
    ! [X1,X2,X3,X4] :
      ( ! [X5,X6] :
          ( in(ordered_pair(X5,X6),cartesian_product2(X1,X2))
        <=> in(ordered_pair(X5,X6),cartesian_product2(X3,X4)) )
     => cartesian_product2(X1,X2) = cartesian_product2(X3,X4) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t108_zfmisc_1) ).

fof(d2_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( X3 = cartesian_product2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ? [X5,X6] :
              ( in(X5,X1)
              & in(X6,X2)
              & X4 = ordered_pair(X5,X6) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_zfmisc_1) ).

fof(t2_tarski,axiom,
    ! [X1,X2] :
      ( ! [X3] :
          ( in(X3,X1)
        <=> in(X3,X2) )
     => X1 = X2 ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_tarski) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ! [X5,X6] :
            ( in(ordered_pair(X5,X6),cartesian_product2(X1,X2))
          <=> in(ordered_pair(X5,X6),cartesian_product2(X3,X4)) )
       => cartesian_product2(X1,X2) = cartesian_product2(X3,X4) ),
    inference(assume_negation,[status(cth)],[t108_zfmisc_1]) ).

fof(c_0_4,negated_conjecture,
    ! [X11,X12,X11,X12] :
      ( ( ~ in(ordered_pair(X11,X12),cartesian_product2(esk1_0,esk2_0))
        | in(ordered_pair(X11,X12),cartesian_product2(esk3_0,esk4_0)) )
      & ( ~ in(ordered_pair(X11,X12),cartesian_product2(esk3_0,esk4_0))
        | in(ordered_pair(X11,X12),cartesian_product2(esk1_0,esk2_0)) )
      & cartesian_product2(esk1_0,esk2_0) != cartesian_product2(esk3_0,esk4_0) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])])]) ).

fof(c_0_5,plain,
    ! [X7,X8,X9,X10,X10,X13,X14,X7,X8,X9,X16,X17] :
      ( ( in(esk5_4(X7,X8,X9,X10),X7)
        | ~ in(X10,X9)
        | X9 != cartesian_product2(X7,X8) )
      & ( in(esk6_4(X7,X8,X9,X10),X8)
        | ~ in(X10,X9)
        | X9 != cartesian_product2(X7,X8) )
      & ( X10 = ordered_pair(esk5_4(X7,X8,X9,X10),esk6_4(X7,X8,X9,X10))
        | ~ in(X10,X9)
        | X9 != cartesian_product2(X7,X8) )
      & ( ~ in(X13,X7)
        | ~ in(X14,X8)
        | X10 != ordered_pair(X13,X14)
        | in(X10,X9)
        | X9 != cartesian_product2(X7,X8) )
      & ( ~ in(esk7_3(X7,X8,X9),X9)
        | ~ in(X16,X7)
        | ~ in(X17,X8)
        | esk7_3(X7,X8,X9) != ordered_pair(X16,X17)
        | X9 = cartesian_product2(X7,X8) )
      & ( in(esk8_3(X7,X8,X9),X7)
        | in(esk7_3(X7,X8,X9),X9)
        | X9 = cartesian_product2(X7,X8) )
      & ( in(esk9_3(X7,X8,X9),X8)
        | in(esk7_3(X7,X8,X9),X9)
        | X9 = cartesian_product2(X7,X8) )
      & ( esk7_3(X7,X8,X9) = ordered_pair(esk8_3(X7,X8,X9),esk9_3(X7,X8,X9))
        | in(esk7_3(X7,X8,X9),X9)
        | X9 = cartesian_product2(X7,X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_zfmisc_1])])])])])])]) ).

cnf(c_0_6,negated_conjecture,
    ( in(ordered_pair(X1,X2),cartesian_product2(esk1_0,esk2_0))
    | ~ in(ordered_pair(X1,X2),cartesian_product2(esk3_0,esk4_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,plain,
    ( X4 = ordered_pair(esk5_4(X2,X3,X1,X4),esk6_4(X2,X3,X1,X4))
    | X1 != cartesian_product2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_8,plain,
    ! [X4,X5] :
      ( ( ~ in(esk10_2(X4,X5),X4)
        | ~ in(esk10_2(X4,X5),X5)
        | X4 = X5 )
      & ( in(esk10_2(X4,X5),X4)
        | in(esk10_2(X4,X5),X5)
        | X4 = X5 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])])])]) ).

cnf(c_0_9,negated_conjecture,
    ( in(X1,cartesian_product2(esk1_0,esk2_0))
    | X2 != cartesian_product2(X3,X4)
    | ~ in(X1,cartesian_product2(esk3_0,esk4_0))
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,plain,
    ( X1 = X2
    | in(esk10_2(X1,X2),X2)
    | in(esk10_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    ( cartesian_product2(esk3_0,esk4_0) = X1
    | in(esk10_2(cartesian_product2(esk3_0,esk4_0),X1),cartesian_product2(esk1_0,esk2_0))
    | in(esk10_2(cartesian_product2(esk3_0,esk4_0),X1),X1)
    | X2 != cartesian_product2(X3,X4)
    | ~ in(esk10_2(cartesian_product2(esk3_0,esk4_0),X1),X2) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_12,negated_conjecture,
    ( in(ordered_pair(X1,X2),cartesian_product2(esk3_0,esk4_0))
    | ~ in(ordered_pair(X1,X2),cartesian_product2(esk1_0,esk2_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_13,negated_conjecture,
    ( cartesian_product2(esk3_0,esk4_0) = X1
    | in(esk10_2(cartesian_product2(esk3_0,esk4_0),X1),cartesian_product2(esk1_0,esk2_0))
    | in(esk10_2(cartesian_product2(esk3_0,esk4_0),X1),X1)
    | cartesian_product2(esk3_0,esk4_0) != cartesian_product2(X2,X3) ),
    inference(spm,[status(thm)],[c_0_11,c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    ( in(X1,cartesian_product2(esk3_0,esk4_0))
    | X2 != cartesian_product2(X3,X4)
    | ~ in(X1,cartesian_product2(esk1_0,esk2_0))
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_7]) ).

cnf(c_0_15,negated_conjecture,
    ( cartesian_product2(esk3_0,esk4_0) = X1
    | in(esk10_2(cartesian_product2(esk3_0,esk4_0),X1),cartesian_product2(esk1_0,esk2_0))
    | in(esk10_2(cartesian_product2(esk3_0,esk4_0),X1),X1) ),
    inference(er,[status(thm)],[c_0_13]) ).

cnf(c_0_16,negated_conjecture,
    cartesian_product2(esk1_0,esk2_0) != cartesian_product2(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_17,negated_conjecture,
    ( in(X1,cartesian_product2(esk3_0,esk4_0))
    | ~ in(X1,cartesian_product2(esk1_0,esk2_0))
    | ~ in(X1,cartesian_product2(X2,X3)) ),
    inference(er,[status(thm)],[c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    in(esk10_2(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk1_0,esk2_0)),cartesian_product2(esk1_0,esk2_0)),
    inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_15]),c_0_16]) ).

cnf(c_0_19,plain,
    ( X1 = X2
    | ~ in(esk10_2(X1,X2),X2)
    | ~ in(esk10_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_20,negated_conjecture,
    in(esk10_2(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk1_0,esk2_0)),cartesian_product2(esk3_0,esk4_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_18])]) ).

cnf(c_0_21,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_16]),c_0_20])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : SET955+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.09/0.12  % Command  : run_ET %s %d
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 21:49:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.23/1.40  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.40  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.40  # Preprocessing time       : 0.015 s
% 0.23/1.40  
% 0.23/1.40  # Proof found!
% 0.23/1.40  # SZS status Theorem
% 0.23/1.40  # SZS output start CNFRefutation
% See solution above
% 0.23/1.40  # Proof object total steps             : 22
% 0.23/1.40  # Proof object clause steps            : 15
% 0.23/1.40  # Proof object formula steps           : 7
% 0.23/1.40  # Proof object conjectures             : 15
% 0.23/1.40  # Proof object clause conjectures      : 12
% 0.23/1.40  # Proof object formula conjectures     : 3
% 0.23/1.40  # Proof object initial clauses used    : 6
% 0.23/1.40  # Proof object initial formulas used   : 3
% 0.23/1.40  # Proof object generating inferences   : 9
% 0.23/1.40  # Proof object simplifying inferences  : 6
% 0.23/1.40  # Training examples: 0 positive, 0 negative
% 0.23/1.40  # Parsed axioms                        : 9
% 0.23/1.40  # Removed by relevancy pruning/SinE    : 2
% 0.23/1.40  # Initial clauses                      : 17
% 0.23/1.40  # Removed in clause preprocessing      : 0
% 0.23/1.40  # Initial clauses in saturation        : 17
% 0.23/1.40  # Processed clauses                    : 56
% 0.23/1.40  # ...of these trivial                  : 1
% 0.23/1.40  # ...subsumed                          : 9
% 0.23/1.40  # ...remaining for further processing  : 45
% 0.23/1.40  # Other redundant clauses eliminated   : 1
% 0.23/1.40  # Clauses deleted for lack of memory   : 0
% 0.23/1.40  # Backward-subsumed                    : 2
% 0.23/1.40  # Backward-rewritten                   : 0
% 0.23/1.40  # Generated clauses                    : 98
% 0.23/1.40  # ...of the previous two non-trivial   : 89
% 0.23/1.40  # Contextual simplify-reflections      : 7
% 0.23/1.40  # Paramodulations                      : 88
% 0.23/1.40  # Factorizations                       : 4
% 0.23/1.40  # Equation resolutions                 : 6
% 0.23/1.40  # Current number of processed clauses  : 43
% 0.23/1.40  #    Positive orientable unit clauses  : 3
% 0.23/1.40  #    Positive unorientable unit clauses: 0
% 0.23/1.40  #    Negative unit clauses             : 5
% 0.23/1.40  #    Non-unit-clauses                  : 35
% 0.23/1.40  # Current number of unprocessed clauses: 47
% 0.23/1.40  # ...number of literals in the above   : 193
% 0.23/1.40  # Current number of archived formulas  : 0
% 0.23/1.40  # Current number of archived clauses   : 2
% 0.23/1.40  # Clause-clause subsumption calls (NU) : 267
% 0.23/1.40  # Rec. Clause-clause subsumption calls : 153
% 0.23/1.40  # Non-unit clause-clause subsumptions  : 15
% 0.23/1.40  # Unit Clause-clause subsumption calls : 4
% 0.23/1.40  # Rewrite failures with RHS unbound    : 0
% 0.23/1.40  # BW rewrite match attempts            : 0
% 0.23/1.40  # BW rewrite match successes           : 0
% 0.23/1.40  # Condensation attempts                : 0
% 0.23/1.40  # Condensation successes               : 0
% 0.23/1.40  # Termbank termtop insertions          : 2988
% 0.23/1.40  
% 0.23/1.40  # -------------------------------------------------
% 0.23/1.40  # User time                : 0.017 s
% 0.23/1.40  # System time              : 0.004 s
% 0.23/1.40  # Total time               : 0.021 s
% 0.23/1.40  # Maximum resident set size: 2960 pages
%------------------------------------------------------------------------------