TSTP Solution File: SET950+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n016.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 00:55:40 EDT 2022

% Result   : Theorem 0.24s 1.43s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   21 (   3 unt;   0 def)
%            Number of atoms       :   94 (  30 equ)
%            Maximal formula atoms :   28 (   4 avg)
%            Number of connectives :  126 (  53   ~;  48   |;  21   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-4 aty)
%            Number of variables   :   69 (   6 sgn  38   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t103_zfmisc_1,conjecture,
    ! [X1,X2,X3,X4] :
      ~ ( subset(X1,cartesian_product2(X2,X3))
        & in(X4,X1)
        & ! [X5,X6] :
            ~ ( in(X5,X2)
              & in(X6,X3)
              & X4 = ordered_pair(X5,X6) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t103_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(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d3_tarski) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ~ ( subset(X1,cartesian_product2(X2,X3))
          & in(X4,X1)
          & ! [X5,X6] :
              ~ ( in(X5,X2)
                & in(X6,X3)
                & X4 = ordered_pair(X5,X6) ) ),
    inference(assume_negation,[status(cth)],[t103_zfmisc_1]) ).

fof(c_0_4,negated_conjecture,
    ! [X11,X12] :
      ( subset(esk1_0,cartesian_product2(esk2_0,esk3_0))
      & in(esk4_0,esk1_0)
      & ( ~ in(X11,esk2_0)
        | ~ in(X12,esk3_0)
        | esk4_0 != ordered_pair(X11,X12) ) ),
    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(esk6_4(X7,X8,X9,X10),X7)
        | ~ in(X10,X9)
        | X9 != cartesian_product2(X7,X8) )
      & ( in(esk7_4(X7,X8,X9,X10),X8)
        | ~ in(X10,X9)
        | X9 != cartesian_product2(X7,X8) )
      & ( X10 = ordered_pair(esk6_4(X7,X8,X9,X10),esk7_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(esk8_3(X7,X8,X9),X9)
        | ~ in(X16,X7)
        | ~ in(X17,X8)
        | esk8_3(X7,X8,X9) != ordered_pair(X16,X17)
        | X9 = cartesian_product2(X7,X8) )
      & ( in(esk9_3(X7,X8,X9),X7)
        | in(esk8_3(X7,X8,X9),X9)
        | X9 = cartesian_product2(X7,X8) )
      & ( in(esk10_3(X7,X8,X9),X8)
        | in(esk8_3(X7,X8,X9),X9)
        | X9 = cartesian_product2(X7,X8) )
      & ( esk8_3(X7,X8,X9) = ordered_pair(esk9_3(X7,X8,X9),esk10_3(X7,X8,X9))
        | in(esk8_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,
    ( esk4_0 != ordered_pair(X1,X2)
    | ~ in(X2,esk3_0)
    | ~ in(X1,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,plain,
    ( X4 = ordered_pair(esk6_4(X2,X3,X1,X4),esk7_4(X2,X3,X1,X4))
    | X1 != cartesian_product2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    ( X1 != cartesian_product2(X2,X3)
    | X4 != esk4_0
    | ~ in(esk7_4(X2,X3,X1,X4),esk3_0)
    | ~ in(esk6_4(X2,X3,X1,X4),esk2_0)
    | ~ in(X4,X1) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_9,plain,
    ( in(esk7_4(X2,X3,X1,X4),X3)
    | X1 != cartesian_product2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,negated_conjecture,
    ( X1 != cartesian_product2(X2,esk3_0)
    | X3 != esk4_0
    | ~ in(esk6_4(X2,esk3_0,X1,X3),esk2_0)
    | ~ in(X3,X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,plain,
    ( in(esk6_4(X2,X3,X1,X4),X2)
    | X1 != cartesian_product2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_12,plain,
    ! [X4,X5,X6,X4,X5] :
      ( ( ~ subset(X4,X5)
        | ~ in(X6,X4)
        | in(X6,X5) )
      & ( in(esk5_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ in(esk5_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    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)],[d3_tarski])])])])])])]) ).

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

cnf(c_0_14,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_15,negated_conjecture,
    subset(esk1_0,cartesian_product2(esk2_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_16,negated_conjecture,
    ( X1 != esk4_0
    | ~ in(X1,cartesian_product2(esk2_0,esk3_0)) ),
    inference(er,[status(thm)],[c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    ( in(X1,cartesian_product2(esk2_0,esk3_0))
    | ~ in(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    ( X1 != esk4_0
    | ~ in(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_19,negated_conjecture,
    in(esk4_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14  % Command  : run_ET %s %d
% 0.13/0.35  % Computer : n016.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  : 600
% 0.13/0.35  % DateTime : Sun Jul 10 03:35:25 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.24/1.43  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.43  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.43  # Preprocessing time       : 0.016 s
% 0.24/1.43  
% 0.24/1.43  # Proof found!
% 0.24/1.43  # SZS status Theorem
% 0.24/1.43  # SZS output start CNFRefutation
% See solution above
% 0.24/1.43  # Proof object total steps             : 21
% 0.24/1.43  # Proof object clause steps            : 14
% 0.24/1.43  # Proof object formula steps           : 7
% 0.24/1.43  # Proof object conjectures             : 13
% 0.24/1.43  # Proof object clause conjectures      : 10
% 0.24/1.43  # Proof object formula conjectures     : 3
% 0.24/1.43  # Proof object initial clauses used    : 7
% 0.24/1.43  # Proof object initial formulas used   : 3
% 0.24/1.43  # Proof object generating inferences   : 7
% 0.24/1.43  # Proof object simplifying inferences  : 0
% 0.24/1.43  # Training examples: 0 positive, 0 negative
% 0.24/1.43  # Parsed axioms                        : 10
% 0.24/1.43  # Removed by relevancy pruning/SinE    : 2
% 0.24/1.43  # Initial clauses                      : 19
% 0.24/1.43  # Removed in clause preprocessing      : 0
% 0.24/1.43  # Initial clauses in saturation        : 19
% 0.24/1.43  # Processed clauses                    : 61
% 0.24/1.43  # ...of these trivial                  : 0
% 0.24/1.43  # ...subsumed                          : 1
% 0.24/1.43  # ...remaining for further processing  : 60
% 0.24/1.43  # Other redundant clauses eliminated   : 1
% 0.24/1.43  # Clauses deleted for lack of memory   : 0
% 0.24/1.43  # Backward-subsumed                    : 0
% 0.24/1.43  # Backward-rewritten                   : 0
% 0.24/1.43  # Generated clauses                    : 69
% 0.24/1.43  # ...of the previous two non-trivial   : 64
% 0.24/1.43  # Contextual simplify-reflections      : 0
% 0.24/1.43  # Paramodulations                      : 64
% 0.24/1.43  # Factorizations                       : 0
% 0.24/1.43  # Equation resolutions                 : 5
% 0.24/1.43  # Current number of processed clauses  : 60
% 0.24/1.43  #    Positive orientable unit clauses  : 4
% 0.24/1.43  #    Positive unorientable unit clauses: 0
% 0.24/1.43  #    Negative unit clauses             : 5
% 0.24/1.43  #    Non-unit-clauses                  : 51
% 0.24/1.43  # Current number of unprocessed clauses: 22
% 0.24/1.43  # ...number of literals in the above   : 94
% 0.24/1.43  # Current number of archived formulas  : 0
% 0.24/1.43  # Current number of archived clauses   : 0
% 0.24/1.43  # Clause-clause subsumption calls (NU) : 676
% 0.24/1.43  # Rec. Clause-clause subsumption calls : 163
% 0.24/1.43  # Non-unit clause-clause subsumptions  : 0
% 0.24/1.43  # Unit Clause-clause subsumption calls : 24
% 0.24/1.43  # Rewrite failures with RHS unbound    : 0
% 0.24/1.43  # BW rewrite match attempts            : 0
% 0.24/1.43  # BW rewrite match successes           : 0
% 0.24/1.43  # Condensation attempts                : 0
% 0.24/1.43  # Condensation successes               : 0
% 0.24/1.43  # Termbank termtop insertions          : 2499
% 0.24/1.43  
% 0.24/1.43  # -------------------------------------------------
% 0.24/1.43  # User time                : 0.020 s
% 0.24/1.43  # System time              : 0.001 s
% 0.24/1.43  # Total time               : 0.021 s
% 0.24/1.43  # Maximum resident set size: 2972 pages
%------------------------------------------------------------------------------