TSTP Solution File: SET975+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n024.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 00:55:49 EDT 2022

% Result   : Theorem 0.22s 1.41s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   25 (   5 unt;   0 def)
%            Number of atoms       :   75 (  28 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :   83 (  33   ~;  35   |;  10   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 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   :   51 (  11 sgn  29   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t128_zfmisc_1,conjecture,
    ! [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(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/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l55_zfmisc_1) ).

fof(d1_tarski,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_tarski) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),X4))
      <=> ( X1 = X3
          & in(X2,X4) ) ),
    inference(assume_negation,[status(cth)],[t128_zfmisc_1]) ).

fof(c_0_4,plain,
    ! [X5,X6,X7,X8,X5,X6,X7,X8] :
      ( ( in(X5,X7)
        | ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
      & ( in(X6,X8)
        | ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
      & ( ~ in(X5,X7)
        | ~ in(X6,X8)
        | in(ordered_pair(X5,X6),cartesian_product2(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)],[l55_zfmisc_1])])])])]) ).

fof(c_0_5,negated_conjecture,
    ( ( ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(singleton(esk3_0),esk4_0))
      | esk1_0 != esk3_0
      | ~ in(esk2_0,esk4_0) )
    & ( esk1_0 = esk3_0
      | in(ordered_pair(esk1_0,esk2_0),cartesian_product2(singleton(esk3_0),esk4_0)) )
    & ( in(esk2_0,esk4_0)
      | in(ordered_pair(esk1_0,esk2_0),cartesian_product2(singleton(esk3_0),esk4_0)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).

fof(c_0_6,plain,
    ! [X4,X5,X6,X6,X4,X5] :
      ( ( ~ in(X6,X5)
        | X6 = X4
        | X5 != singleton(X4) )
      & ( X6 != X4
        | in(X6,X5)
        | X5 != singleton(X4) )
      & ( ~ in(esk5_2(X4,X5),X5)
        | esk5_2(X4,X5) != X4
        | X5 = singleton(X4) )
      & ( in(esk5_2(X4,X5),X5)
        | esk5_2(X4,X5) = X4
        | X5 = singleton(X4) ) ),
    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)],[d1_tarski])])])])])])]) ).

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

cnf(c_0_8,negated_conjecture,
    ( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(singleton(esk3_0),esk4_0))
    | esk1_0 = esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    ( ~ in(esk2_0,esk4_0)
    | esk1_0 != esk3_0
    | ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(singleton(esk3_0),esk4_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

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

cnf(c_0_11,plain,
    ( in(X2,X4)
    | ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_12,negated_conjecture,
    ( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(singleton(esk3_0),esk4_0))
    | in(esk2_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_13,plain,
    ( X3 = X2
    | X1 != singleton(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_14,negated_conjecture,
    ( esk1_0 = esk3_0
    | in(esk1_0,singleton(esk3_0)) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    ( esk1_0 != esk3_0
    | ~ in(esk1_0,singleton(esk3_0))
    | ~ in(esk2_0,esk4_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    in(esk2_0,esk4_0),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_17,negated_conjecture,
    ( esk1_0 = esk3_0
    | X1 = esk1_0
    | singleton(esk3_0) != singleton(X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,plain,
    ( in(X3,X1)
    | X1 != singleton(X2)
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_19,negated_conjecture,
    ( esk1_0 != esk3_0
    | ~ in(esk1_0,singleton(esk3_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).

cnf(c_0_20,negated_conjecture,
    esk1_0 = esk3_0,
    inference(er,[status(thm)],[c_0_17]) ).

cnf(c_0_21,plain,
    ( in(X1,X2)
    | X2 != singleton(X1) ),
    inference(er,[status(thm)],[c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    ~ in(esk3_0,singleton(esk3_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20])]) ).

cnf(c_0_23,plain,
    in(X1,singleton(X1)),
    inference(er,[status(thm)],[c_0_21]) ).

cnf(c_0_24,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : run_ET %s %d
% 0.12/0.33  % Computer : n024.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 12:58:43 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.22/1.41  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.41  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.41  # Preprocessing time       : 0.015 s
% 0.22/1.41  
% 0.22/1.41  # Proof found!
% 0.22/1.41  # SZS status Theorem
% 0.22/1.41  # SZS output start CNFRefutation
% See solution above
% 0.22/1.41  # Proof object total steps             : 25
% 0.22/1.41  # Proof object clause steps            : 18
% 0.22/1.41  # Proof object formula steps           : 7
% 0.22/1.41  # Proof object conjectures             : 14
% 0.22/1.41  # Proof object clause conjectures      : 11
% 0.22/1.41  # Proof object formula conjectures     : 3
% 0.22/1.41  # Proof object initial clauses used    : 8
% 0.22/1.41  # Proof object initial formulas used   : 3
% 0.22/1.41  # Proof object generating inferences   : 6
% 0.22/1.41  # Proof object simplifying inferences  : 8
% 0.22/1.41  # Training examples: 0 positive, 0 negative
% 0.22/1.41  # Parsed axioms                        : 9
% 0.22/1.41  # Removed by relevancy pruning/SinE    : 2
% 0.22/1.41  # Initial clauses                      : 14
% 0.22/1.41  # Removed in clause preprocessing      : 0
% 0.22/1.41  # Initial clauses in saturation        : 14
% 0.22/1.41  # Processed clauses                    : 32
% 0.22/1.41  # ...of these trivial                  : 1
% 0.22/1.41  # ...subsumed                          : 1
% 0.22/1.41  # ...remaining for further processing  : 30
% 0.22/1.41  # Other redundant clauses eliminated   : 1
% 0.22/1.41  # Clauses deleted for lack of memory   : 0
% 0.22/1.41  # Backward-subsumed                    : 0
% 0.22/1.41  # Backward-rewritten                   : 12
% 0.22/1.41  # Generated clauses                    : 36
% 0.22/1.41  # ...of the previous two non-trivial   : 30
% 0.22/1.41  # Contextual simplify-reflections      : 0
% 0.22/1.41  # Paramodulations                      : 33
% 0.22/1.41  # Factorizations                       : 0
% 0.22/1.41  # Equation resolutions                 : 3
% 0.22/1.41  # Current number of processed clauses  : 17
% 0.22/1.41  #    Positive orientable unit clauses  : 4
% 0.22/1.41  #    Positive unorientable unit clauses: 0
% 0.22/1.41  #    Negative unit clauses             : 3
% 0.22/1.41  #    Non-unit-clauses                  : 10
% 0.22/1.41  # Current number of unprocessed clauses: 7
% 0.22/1.41  # ...number of literals in the above   : 24
% 0.22/1.41  # Current number of archived formulas  : 0
% 0.22/1.41  # Current number of archived clauses   : 12
% 0.22/1.41  # Clause-clause subsumption calls (NU) : 62
% 0.22/1.41  # Rec. Clause-clause subsumption calls : 57
% 0.22/1.41  # Non-unit clause-clause subsumptions  : 1
% 0.22/1.41  # Unit Clause-clause subsumption calls : 10
% 0.22/1.41  # Rewrite failures with RHS unbound    : 0
% 0.22/1.41  # BW rewrite match attempts            : 3
% 0.22/1.41  # BW rewrite match successes           : 3
% 0.22/1.41  # Condensation attempts                : 0
% 0.22/1.41  # Condensation successes               : 0
% 0.22/1.41  # Termbank termtop insertions          : 1157
% 0.22/1.41  
% 0.22/1.41  # -------------------------------------------------
% 0.22/1.41  # User time                : 0.013 s
% 0.22/1.41  # System time              : 0.004 s
% 0.22/1.41  # Total time               : 0.017 s
% 0.22/1.41  # Maximum resident set size: 2772 pages
%------------------------------------------------------------------------------