TSTP Solution File: SET974+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET974+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n017.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 00:55:48 EDT 2022

% Result   : Theorem 0.23s 1.42s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   30 (   8 unt;   0 def)
%            Number of atoms       :   65 (   5 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   61 (  26   ~;  22   |;  10   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-5 aty)
%            Number of variables   :   80 (  17 sgn  36   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t4_xboole_0,axiom,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
      & ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
          & disjoint(X1,X2) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t4_xboole_0) ).

fof(t104_zfmisc_1,axiom,
    ! [X1,X2,X3,X4,X5] :
      ~ ( in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5)))
        & ! [X6,X7] :
            ~ ( X1 = ordered_pair(X6,X7)
              & in(X6,set_intersection2(X2,X4))
              & in(X7,set_intersection2(X3,X5)) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t104_zfmisc_1) ).

fof(commutativity_k3_xboole_0,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k3_xboole_0) ).

fof(t127_zfmisc_1,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( disjoint(X1,X2)
        | disjoint(X3,X4) )
     => disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t127_zfmisc_1) ).

fof(symmetry_r1_xboole_0,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
     => disjoint(X2,X1) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',symmetry_r1_xboole_0) ).

fof(c_0_5,plain,
    ! [X4,X5,X4,X5,X7] :
      ( ( disjoint(X4,X5)
        | in(esk5_2(X4,X5),set_intersection2(X4,X5)) )
      & ( ~ in(X7,set_intersection2(X4,X5))
        | ~ disjoint(X4,X5) ) ),
    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)],[t4_xboole_0])])])])])])]) ).

fof(c_0_6,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ( X8 = ordered_pair(esk6_5(X8,X9,X10,X11,X12),esk7_5(X8,X9,X10,X11,X12))
        | ~ in(X8,set_intersection2(cartesian_product2(X9,X10),cartesian_product2(X11,X12))) )
      & ( in(esk6_5(X8,X9,X10,X11,X12),set_intersection2(X9,X11))
        | ~ in(X8,set_intersection2(cartesian_product2(X9,X10),cartesian_product2(X11,X12))) )
      & ( in(esk7_5(X8,X9,X10,X11,X12),set_intersection2(X10,X12))
        | ~ in(X8,set_intersection2(cartesian_product2(X9,X10),cartesian_product2(X11,X12))) ) ),
    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)],[t104_zfmisc_1])])])])])]) ).

fof(c_0_7,plain,
    ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).

fof(c_0_8,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( disjoint(X1,X2)
          | disjoint(X3,X4) )
       => disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
    inference(assume_negation,[status(cth)],[t127_zfmisc_1]) ).

cnf(c_0_9,plain,
    ( ~ disjoint(X1,X2)
    | ~ in(X3,set_intersection2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    ( in(esk7_5(X1,X2,X3,X4,X5),set_intersection2(X3,X5))
    | ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( in(esk5_2(X1,X2),set_intersection2(X1,X2))
    | disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_13,plain,
    ! [X3,X4] :
      ( ~ disjoint(X3,X4)
      | disjoint(X4,X3) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).

fof(c_0_14,negated_conjecture,
    ( ( disjoint(esk1_0,esk2_0)
      | disjoint(esk3_0,esk4_0) )
    & ~ disjoint(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk2_0,esk4_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

cnf(c_0_15,plain,
    ( ~ disjoint(X1,X2)
    | ~ in(X3,set_intersection2(cartesian_product2(X4,X1),cartesian_product2(X5,X2))) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_16,plain,
    ( disjoint(X1,X2)
    | in(esk5_2(X1,X2),set_intersection2(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_17,plain,
    ( disjoint(X1,X2)
    | ~ disjoint(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_18,negated_conjecture,
    ( disjoint(esk3_0,esk4_0)
    | disjoint(esk1_0,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_19,plain,
    ( disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
    | ~ disjoint(X4,X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_20,negated_conjecture,
    ( disjoint(esk1_0,esk2_0)
    | disjoint(esk4_0,esk3_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,plain,
    ( in(esk6_5(X1,X2,X3,X4,X5),set_intersection2(X2,X4))
    | ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_22,negated_conjecture,
    ~ disjoint(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk2_0,esk4_0)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_23,negated_conjecture,
    ( disjoint(cartesian_product2(X1,esk3_0),cartesian_product2(X2,esk4_0))
    | disjoint(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,plain,
    ( ~ disjoint(X1,X2)
    | ~ in(X3,set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X5))) ),
    inference(spm,[status(thm)],[c_0_9,c_0_21]) ).

cnf(c_0_25,negated_conjecture,
    disjoint(esk1_0,esk2_0),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_26,plain,
    ( disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
    | ~ disjoint(X3,X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_16]) ).

cnf(c_0_27,negated_conjecture,
    disjoint(esk2_0,esk1_0),
    inference(spm,[status(thm)],[c_0_17,c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    disjoint(cartesian_product2(esk1_0,X1),cartesian_product2(esk2_0,X2)),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_29,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_28])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET974+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13  % Command  : run_ET %s %d
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul 10 14:26:18 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.23/1.42  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.42  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.42  # Preprocessing time       : 0.016 s
% 0.23/1.42  
% 0.23/1.42  # Proof found!
% 0.23/1.42  # SZS status Theorem
% 0.23/1.42  # SZS output start CNFRefutation
% See solution above
% 0.23/1.42  # Proof object total steps             : 30
% 0.23/1.42  # Proof object clause steps            : 19
% 0.23/1.42  # Proof object formula steps           : 11
% 0.23/1.42  # Proof object conjectures             : 11
% 0.23/1.42  # Proof object clause conjectures      : 8
% 0.23/1.42  # Proof object formula conjectures     : 3
% 0.23/1.42  # Proof object initial clauses used    : 8
% 0.23/1.42  # Proof object initial formulas used   : 5
% 0.23/1.42  # Proof object generating inferences   : 10
% 0.23/1.42  # Proof object simplifying inferences  : 2
% 0.23/1.42  # Training examples: 0 positive, 0 negative
% 0.23/1.42  # Parsed axioms                        : 12
% 0.23/1.42  # Removed by relevancy pruning/SinE    : 2
% 0.23/1.42  # Initial clauses                      : 14
% 0.23/1.42  # Removed in clause preprocessing      : 0
% 0.23/1.42  # Initial clauses in saturation        : 14
% 0.23/1.42  # Processed clauses                    : 82
% 0.23/1.42  # ...of these trivial                  : 2
% 0.23/1.42  # ...subsumed                          : 32
% 0.23/1.42  # ...remaining for further processing  : 48
% 0.23/1.42  # Other redundant clauses eliminated   : 0
% 0.23/1.42  # Clauses deleted for lack of memory   : 0
% 0.23/1.42  # Backward-subsumed                    : 0
% 0.23/1.42  # Backward-rewritten                   : 4
% 0.23/1.42  # Generated clauses                    : 162
% 0.23/1.42  # ...of the previous two non-trivial   : 148
% 0.23/1.42  # Contextual simplify-reflections      : 0
% 0.23/1.42  # Paramodulations                      : 162
% 0.23/1.42  # Factorizations                       : 0
% 0.23/1.42  # Equation resolutions                 : 0
% 0.23/1.42  # Current number of processed clauses  : 44
% 0.23/1.42  #    Positive orientable unit clauses  : 9
% 0.23/1.42  #    Positive unorientable unit clauses: 1
% 0.23/1.42  #    Negative unit clauses             : 2
% 0.23/1.42  #    Non-unit-clauses                  : 32
% 0.23/1.42  # Current number of unprocessed clauses: 77
% 0.23/1.42  # ...number of literals in the above   : 147
% 0.23/1.42  # Current number of archived formulas  : 0
% 0.23/1.42  # Current number of archived clauses   : 4
% 0.23/1.42  # Clause-clause subsumption calls (NU) : 232
% 0.23/1.42  # Rec. Clause-clause subsumption calls : 215
% 0.23/1.42  # Non-unit clause-clause subsumptions  : 32
% 0.23/1.42  # Unit Clause-clause subsumption calls : 1
% 0.23/1.42  # Rewrite failures with RHS unbound    : 0
% 0.23/1.42  # BW rewrite match attempts            : 5
% 0.23/1.42  # BW rewrite match successes           : 4
% 0.23/1.42  # Condensation attempts                : 0
% 0.23/1.42  # Condensation successes               : 0
% 0.23/1.42  # Termbank termtop insertions          : 2507
% 0.23/1.42  
% 0.23/1.42  # -------------------------------------------------
% 0.23/1.42  # User time                : 0.017 s
% 0.23/1.42  # System time              : 0.003 s
% 0.23/1.42  # Total time               : 0.020 s
% 0.23/1.42  # Maximum resident set size: 2928 pages
%------------------------------------------------------------------------------