TSTP Solution File: SET587+3 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n006.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 00:52:11 EDT 2022

% Result   : Theorem 0.24s 1.43s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   32 (   7 unt;   0 def)
%            Number of atoms       :   80 (  14 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   78 (  30   ~;  34   |;   7   &)
%                                         (   5 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   60 (  10 sgn  28   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(prove_difference_empty_set,conjecture,
    ! [X1,X2] :
      ( difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_difference_empty_set) ).

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

fof(empty_set_defn,axiom,
    ! [X1] : ~ member(X1,empty_set),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',empty_set_defn) ).

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

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

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2] :
        ( difference(X1,X2) = empty_set
      <=> subset(X1,X2) ),
    inference(assume_negation,[status(cth)],[prove_difference_empty_set]) ).

fof(c_0_6,plain,
    ! [X4,X5,X6,X4,X5,X6] :
      ( ( member(X6,X4)
        | ~ member(X6,difference(X4,X5)) )
      & ( ~ member(X6,X5)
        | ~ member(X6,difference(X4,X5)) )
      & ( ~ member(X6,X4)
        | member(X6,X5)
        | member(X6,difference(X4,X5)) ) ),
    inference(distribute,[status(thm)],[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)],[difference_defn])])])])])]) ).

fof(c_0_7,negated_conjecture,
    ( ( difference(esk1_0,esk2_0) != empty_set
      | ~ subset(esk1_0,esk2_0) )
    & ( difference(esk1_0,esk2_0) = empty_set
      | subset(esk1_0,esk2_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_8,plain,
    ! [X2] : ~ member(X2,empty_set),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[empty_set_defn])]) ).

fof(c_0_9,plain,
    ! [X4,X5,X6,X4,X5] :
      ( ( ~ subset(X4,X5)
        | ~ member(X6,X4)
        | member(X6,X5) )
      & ( member(esk3_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ member(esk3_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)],[subset_defn])])])])])])]) ).

cnf(c_0_10,plain,
    ( member(X1,difference(X2,X3))
    | member(X1,X3)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,negated_conjecture,
    ( subset(esk1_0,esk2_0)
    | difference(esk1_0,esk2_0) = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( subset(X1,X2)
    | ~ member(esk3_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,negated_conjecture,
    ( member(X1,esk2_0)
    | ~ member(X1,esk1_0) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]) ).

cnf(c_0_16,plain,
    ( member(X1,X2)
    | ~ member(X1,difference(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_17,plain,
    ( subset(X1,X2)
    | member(esk3_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_18,negated_conjecture,
    ( subset(X1,esk2_0)
    | ~ member(esk3_2(X1,esk2_0),esk1_0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,plain,
    ( subset(difference(X1,X2),X3)
    | member(esk3_2(difference(X1,X2),X3),X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

fof(c_0_20,plain,
    ! [X4,X5] :
      ( ( ~ member(esk4_2(X4,X5),X4)
        | ~ member(esk4_2(X4,X5),X5)
        | X4 = X5 )
      & ( member(esk4_2(X4,X5),X4)
        | member(esk4_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)],[member_equal])])])])])]) ).

cnf(c_0_21,negated_conjecture,
    subset(difference(esk1_0,X1),esk2_0),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_22,plain,
    ( X1 = X2
    | member(esk4_2(X1,X2),X2)
    | member(esk4_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_23,plain,
    ( ~ member(X1,difference(X2,X3))
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_24,negated_conjecture,
    ( member(X1,esk2_0)
    | ~ member(X1,difference(esk1_0,X2)) ),
    inference(spm,[status(thm)],[c_0_13,c_0_21]) ).

cnf(c_0_25,plain,
    ( empty_set = X1
    | member(esk4_2(empty_set,X1),X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_22]) ).

cnf(c_0_26,negated_conjecture,
    ( ~ subset(esk1_0,esk2_0)
    | difference(esk1_0,esk2_0) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_27,negated_conjecture,
    subset(esk1_0,esk2_0),
    inference(spm,[status(thm)],[c_0_18,c_0_17]) ).

cnf(c_0_28,plain,
    ( X1 = difference(X2,X3)
    | member(esk4_2(X1,difference(X2,X3)),X1)
    | ~ member(esk4_2(X1,difference(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_23,c_0_22]) ).

cnf(c_0_29,negated_conjecture,
    ( difference(esk1_0,X1) = empty_set
    | member(esk4_2(empty_set,difference(esk1_0,X1)),esk2_0) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_30,negated_conjecture,
    difference(esk1_0,esk2_0) != empty_set,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).

cnf(c_0_31,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_12]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14  % Command  : run_ET %s %d
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sat Jul  9 18:26:06 EDT 2022
% 0.14/0.35  % 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             : 32
% 0.24/1.43  # Proof object clause steps            : 21
% 0.24/1.43  # Proof object formula steps           : 11
% 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    : 10
% 0.24/1.43  # Proof object initial formulas used   : 5
% 0.24/1.43  # Proof object generating inferences   : 10
% 0.24/1.43  # Proof object simplifying inferences  : 6
% 0.24/1.43  # Training examples: 0 positive, 0 negative
% 0.24/1.43  # Parsed axioms                        : 9
% 0.24/1.43  # Removed by relevancy pruning/SinE    : 1
% 0.24/1.43  # Initial clauses                      : 19
% 0.24/1.43  # Removed in clause preprocessing      : 2
% 0.24/1.43  # Initial clauses in saturation        : 17
% 0.24/1.43  # Processed clauses                    : 50
% 0.24/1.43  # ...of these trivial                  : 1
% 0.24/1.43  # ...subsumed                          : 10
% 0.24/1.43  # ...remaining for further processing  : 39
% 0.24/1.43  # Other redundant clauses eliminated   : 2
% 0.24/1.43  # Clauses deleted for lack of memory   : 0
% 0.24/1.43  # Backward-subsumed                    : 0
% 0.24/1.43  # Backward-rewritten                   : 3
% 0.24/1.43  # Generated clauses                    : 110
% 0.24/1.43  # ...of the previous two non-trivial   : 84
% 0.24/1.43  # Contextual simplify-reflections      : 1
% 0.24/1.43  # Paramodulations                      : 102
% 0.24/1.43  # Factorizations                       : 6
% 0.24/1.43  # Equation resolutions                 : 2
% 0.24/1.43  # Current number of processed clauses  : 34
% 0.24/1.43  #    Positive orientable unit clauses  : 7
% 0.24/1.43  #    Positive unorientable unit clauses: 0
% 0.24/1.43  #    Negative unit clauses             : 2
% 0.24/1.43  #    Non-unit-clauses                  : 25
% 0.24/1.43  # Current number of unprocessed clauses: 49
% 0.24/1.43  # ...number of literals in the above   : 130
% 0.24/1.43  # Current number of archived formulas  : 0
% 0.24/1.43  # Current number of archived clauses   : 3
% 0.24/1.43  # Clause-clause subsumption calls (NU) : 65
% 0.24/1.43  # Rec. Clause-clause subsumption calls : 52
% 0.24/1.43  # Non-unit clause-clause subsumptions  : 3
% 0.24/1.43  # Unit Clause-clause subsumption calls : 35
% 0.24/1.43  # Rewrite failures with RHS unbound    : 0
% 0.24/1.43  # BW rewrite match attempts            : 13
% 0.24/1.43  # BW rewrite match successes           : 2
% 0.24/1.43  # Condensation attempts                : 0
% 0.24/1.43  # Condensation successes               : 0
% 0.24/1.43  # Termbank termtop insertions          : 2188
% 0.24/1.43  
% 0.24/1.43  # -------------------------------------------------
% 0.24/1.43  # User time                : 0.017 s
% 0.24/1.43  # System time              : 0.002 s
% 0.24/1.43  # Total time               : 0.019 s
% 0.24/1.43  # Maximum resident set size: 2772 pages
%------------------------------------------------------------------------------