TSTP Solution File: SET977+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET977+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n003.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 00:55:50 EDT 2022

% Result   : Theorem 0.22s 1.40s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   21 (   3 unt;   0 def)
%            Number of atoms       :   58 (  27 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   70 (  33   ~;  22   |;  10   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   57 (  15 sgn  33   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t128_zfmisc_1,axiom,
    ! [X1,X2,X3,X4] :
      ( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),X4))
    <=> ( X1 = X3
        & in(X2,X4) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t128_zfmisc_1) ).

fof(t129_zfmisc_1,axiom,
    ! [X1,X2,X3,X4] :
      ( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
    <=> ( in(X1,X3)
        & X2 = X4 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t129_zfmisc_1) ).

fof(d1_xboole_0,axiom,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_xboole_0) ).

fof(t130_zfmisc_1,conjecture,
    ! [X1,X2] :
      ( X1 != empty_set
     => ( cartesian_product2(singleton(X2),X1) != empty_set
        & cartesian_product2(X1,singleton(X2)) != empty_set ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t130_zfmisc_1) ).

fof(c_0_4,plain,
    ! [X5,X6,X7,X8,X5,X6,X7,X8] :
      ( ( X5 = X7
        | ~ in(ordered_pair(X5,X6),cartesian_product2(singleton(X7),X8)) )
      & ( in(X6,X8)
        | ~ in(ordered_pair(X5,X6),cartesian_product2(singleton(X7),X8)) )
      & ( X5 != X7
        | ~ in(X6,X8)
        | in(ordered_pair(X5,X6),cartesian_product2(singleton(X7),X8)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t128_zfmisc_1])])])])]) ).

fof(c_0_5,plain,
    ! [X5,X6,X7,X8,X5,X6,X7,X8] :
      ( ( in(X5,X7)
        | ~ in(ordered_pair(X5,X6),cartesian_product2(X7,singleton(X8))) )
      & ( X6 = X8
        | ~ in(ordered_pair(X5,X6),cartesian_product2(X7,singleton(X8))) )
      & ( ~ in(X5,X7)
        | X6 != X8
        | in(ordered_pair(X5,X6),cartesian_product2(X7,singleton(X8))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t129_zfmisc_1])])])])]) ).

fof(c_0_6,plain,
    ! [X3,X4,X3] :
      ( ( X3 != empty_set
        | ~ in(X4,X3) )
      & ( in(esk4_1(X3),X3)
        | X3 = empty_set ) ),
    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)],[inference(fof_simplification,[status(thm)],[d1_xboole_0])])])])])])]) ).

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

fof(c_0_8,negated_conjecture,
    ~ ! [X1,X2] :
        ( X1 != empty_set
       => ( cartesian_product2(singleton(X2),X1) != empty_set
          & cartesian_product2(X1,singleton(X2)) != empty_set ) ),
    inference(assume_negation,[status(cth)],[t130_zfmisc_1]) ).

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

cnf(c_0_10,plain,
    ( ~ in(X1,X2)
    | X2 != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( in(ordered_pair(X1,X2),cartesian_product2(singleton(X1),X3))
    | ~ in(X2,X3) ),
    inference(er,[status(thm)],[c_0_7]) ).

fof(c_0_12,negated_conjecture,
    ( esk1_0 != empty_set
    & ( cartesian_product2(singleton(esk2_0),esk1_0) = empty_set
      | cartesian_product2(esk1_0,singleton(esk3_0)) = empty_set ) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).

cnf(c_0_13,plain,
    ( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X2)))
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( cartesian_product2(singleton(X1),X2) != empty_set
    | ~ in(X3,X2) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    ( cartesian_product2(esk1_0,singleton(esk3_0)) = empty_set
    | cartesian_product2(singleton(esk2_0),esk1_0) = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_16,plain,
    ( cartesian_product2(X1,singleton(X2)) != empty_set
    | ~ in(X3,X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    ~ in(X1,esk1_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).

cnf(c_0_18,plain,
    ( X1 = empty_set
    | in(esk4_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_19,negated_conjecture,
    esk1_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SET977+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : run_ET %s %d
% 0.13/0.33  % Computer : n003.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  : 600
% 0.13/0.33  % DateTime : Sat Jul  9 22:40:14 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.22/1.40  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.40  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.40  # Preprocessing time       : 0.015 s
% 0.22/1.40  
% 0.22/1.40  # Proof found!
% 0.22/1.40  # SZS status Theorem
% 0.22/1.40  # SZS output start CNFRefutation
% See solution above
% 0.22/1.40  # Proof object total steps             : 21
% 0.22/1.40  # Proof object clause steps            : 12
% 0.22/1.40  # Proof object formula steps           : 9
% 0.22/1.40  # Proof object conjectures             : 7
% 0.22/1.40  # Proof object clause conjectures      : 4
% 0.22/1.40  # Proof object formula conjectures     : 3
% 0.22/1.40  # Proof object initial clauses used    : 6
% 0.22/1.40  # Proof object initial formulas used   : 4
% 0.22/1.40  # Proof object generating inferences   : 4
% 0.22/1.40  # Proof object simplifying inferences  : 4
% 0.22/1.40  # Training examples: 0 positive, 0 negative
% 0.22/1.40  # Parsed axioms                        : 11
% 0.22/1.40  # Removed by relevancy pruning/SinE    : 2
% 0.22/1.40  # Initial clauses                      : 15
% 0.22/1.40  # Removed in clause preprocessing      : 0
% 0.22/1.40  # Initial clauses in saturation        : 15
% 0.22/1.40  # Processed clauses                    : 24
% 0.22/1.40  # ...of these trivial                  : 0
% 0.22/1.40  # ...subsumed                          : 0
% 0.22/1.40  # ...remaining for further processing  : 24
% 0.22/1.40  # Other redundant clauses eliminated   : 2
% 0.22/1.40  # Clauses deleted for lack of memory   : 0
% 0.22/1.40  # Backward-subsumed                    : 0
% 0.22/1.40  # Backward-rewritten                   : 0
% 0.22/1.40  # Generated clauses                    : 20
% 0.22/1.40  # ...of the previous two non-trivial   : 16
% 0.22/1.40  # Contextual simplify-reflections      : 1
% 0.22/1.40  # Paramodulations                      : 18
% 0.22/1.40  # Factorizations                       : 0
% 0.22/1.40  # Equation resolutions                 : 2
% 0.22/1.40  # Current number of processed clauses  : 22
% 0.22/1.40  #    Positive orientable unit clauses  : 2
% 0.22/1.40  #    Positive unorientable unit clauses: 0
% 0.22/1.40  #    Negative unit clauses             : 4
% 0.22/1.40  #    Non-unit-clauses                  : 16
% 0.22/1.40  # Current number of unprocessed clauses: 7
% 0.22/1.40  # ...number of literals in the above   : 15
% 0.22/1.40  # Current number of archived formulas  : 0
% 0.22/1.40  # Current number of archived clauses   : 0
% 0.22/1.40  # Clause-clause subsumption calls (NU) : 47
% 0.22/1.40  # Rec. Clause-clause subsumption calls : 45
% 0.22/1.40  # Non-unit clause-clause subsumptions  : 1
% 0.22/1.40  # Unit Clause-clause subsumption calls : 14
% 0.22/1.40  # Rewrite failures with RHS unbound    : 0
% 0.22/1.40  # BW rewrite match attempts            : 0
% 0.22/1.40  # BW rewrite match successes           : 0
% 0.22/1.40  # Condensation attempts                : 0
% 0.22/1.40  # Condensation successes               : 0
% 0.22/1.40  # Termbank termtop insertions          : 980
% 0.22/1.40  
% 0.22/1.40  # -------------------------------------------------
% 0.22/1.40  # User time                : 0.013 s
% 0.22/1.40  # System time              : 0.004 s
% 0.22/1.40  # Total time               : 0.016 s
% 0.22/1.40  # Maximum resident set size: 2776 pages
%------------------------------------------------------------------------------