TSTP Solution File: SET600+3 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n022.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 00:52:20 EDT 2022

% Result   : Theorem 0.23s 1.41s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   32 (   8 unt;   0 def)
%            Number of atoms       :   85 (  40 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :   84 (  31   ~;  39   |;   9   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   47 (  12 sgn  24   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(prove_th59,conjecture,
    ! [X1,X2] :
      ( union(X1,X2) = empty_set
    <=> ( X1 = empty_set
        & X2 = empty_set ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th59) ).

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

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2] :
        ( union(X1,X2) = empty_set
      <=> ( X1 = empty_set
          & X2 = empty_set ) ),
    inference(assume_negation,[status(cth)],[prove_th59]) ).

fof(c_0_5,plain,
    ! [X4,X5,X6,X4,X5,X6] :
      ( ( ~ member(X6,union(X4,X5))
        | member(X6,X4)
        | member(X6,X5) )
      & ( ~ member(X6,X4)
        | member(X6,union(X4,X5)) )
      & ( ~ member(X6,X5)
        | member(X6,union(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)],[union_defn])])])])]) ).

fof(c_0_6,negated_conjecture,
    ( ( union(esk1_0,esk2_0) != empty_set
      | esk1_0 != empty_set
      | esk2_0 != empty_set )
    & ( esk1_0 = empty_set
      | union(esk1_0,esk2_0) = empty_set )
    & ( esk2_0 = empty_set
      | union(esk1_0,esk2_0) = empty_set ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).

fof(c_0_7,plain,
    ! [X2] : ~ member(X2,empty_set),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[empty_set_defn])]) ).

fof(c_0_8,plain,
    ! [X4,X5,X6,X6,X4,X5] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | X4 != X5 )
      & ( ~ member(X6,X5)
        | member(X6,X4)
        | X4 != X5 )
      & ( ~ member(esk3_2(X4,X5),X4)
        | ~ member(esk3_2(X4,X5),X5)
        | X4 = X5 )
      & ( member(esk3_2(X4,X5),X4)
        | member(esk3_2(X4,X5),X5)
        | 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)],[equal_member_defn])])])])])])]) ).

cnf(c_0_9,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,negated_conjecture,
    ( union(esk1_0,esk2_0) = empty_set
    | esk2_0 = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    ( X1 = X2
    | member(esk3_2(X1,X2),X2)
    | member(esk3_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_14,negated_conjecture,
    ( union(esk1_0,esk2_0) = empty_set
    | esk1_0 = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_15,negated_conjecture,
    ( empty_set = esk2_0
    | ~ member(X1,esk2_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).

cnf(c_0_16,plain,
    ( X1 = empty_set
    | member(esk3_2(X1,empty_set),X1) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_17,negated_conjecture,
    ( empty_set = esk1_0
    | ~ member(X1,esk1_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_11]) ).

cnf(c_0_18,negated_conjecture,
    empty_set = esk2_0,
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    ( esk2_0 = esk1_0
    | ~ member(X1,esk1_0) ),
    inference(rw,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_20,plain,
    ( X1 = esk2_0
    | member(esk3_2(X1,esk2_0),X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_18]),c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    esk2_0 = esk1_0,
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_22,plain,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_23,plain,
    ( X1 = esk1_0
    | member(esk3_2(X1,esk1_0),X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).

cnf(c_0_24,negated_conjecture,
    ( esk2_0 != empty_set
    | esk1_0 != empty_set
    | union(esk1_0,esk2_0) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_25,plain,
    ( union(X1,X2) = esk1_0
    | member(esk3_2(union(X1,X2),esk1_0),X1)
    | member(esk3_2(union(X1,X2),esk1_0),X2) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_26,negated_conjecture,
    ( union(esk1_0,esk2_0) != esk2_0
    | esk2_0 != esk1_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_18]),c_0_18]),c_0_18])]) ).

cnf(c_0_27,plain,
    ( X1 = X2
    | ~ member(esk3_2(X1,X2),X2)
    | ~ member(esk3_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_28,plain,
    ( union(X1,X1) = esk1_0
    | member(esk3_2(union(X1,X1),esk1_0),X1) ),
    inference(ef,[status(thm)],[c_0_25]) ).

cnf(c_0_29,negated_conjecture,
    union(esk1_0,esk1_0) != esk1_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_21]),c_0_21]),c_0_21])]) ).

cnf(c_0_30,plain,
    ~ member(esk3_2(union(esk1_0,esk1_0),esk1_0),union(esk1_0,esk1_0)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_31,plain,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_23]),c_0_29]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jul  9 23:20:10 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.23/1.41  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.41  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.41  # Preprocessing time       : 0.014 s
% 0.23/1.41  
% 0.23/1.41  # Proof found!
% 0.23/1.41  # SZS status Theorem
% 0.23/1.41  # SZS output start CNFRefutation
% See solution above
% 0.23/1.41  # Proof object total steps             : 32
% 0.23/1.41  # Proof object clause steps            : 23
% 0.23/1.41  # Proof object formula steps           : 9
% 0.23/1.41  # Proof object conjectures             : 13
% 0.23/1.41  # Proof object clause conjectures      : 10
% 0.23/1.41  # Proof object formula conjectures     : 3
% 0.23/1.41  # Proof object initial clauses used    : 9
% 0.23/1.41  # Proof object initial formulas used   : 4
% 0.23/1.41  # Proof object generating inferences   : 9
% 0.23/1.41  # Proof object simplifying inferences  : 17
% 0.23/1.41  # Training examples: 0 positive, 0 negative
% 0.23/1.41  # Parsed axioms                        : 9
% 0.23/1.41  # Removed by relevancy pruning/SinE    : 4
% 0.23/1.41  # Initial clauses                      : 12
% 0.23/1.41  # Removed in clause preprocessing      : 2
% 0.23/1.41  # Initial clauses in saturation        : 10
% 0.23/1.41  # Processed clauses                    : 41
% 0.23/1.41  # ...of these trivial                  : 0
% 0.23/1.41  # ...subsumed                          : 11
% 0.23/1.41  # ...remaining for further processing  : 30
% 0.23/1.41  # Other redundant clauses eliminated   : 0
% 0.23/1.41  # Clauses deleted for lack of memory   : 0
% 0.23/1.41  # Backward-subsumed                    : 0
% 0.23/1.41  # Backward-rewritten                   : 16
% 0.23/1.41  # Generated clauses                    : 80
% 0.23/1.41  # ...of the previous two non-trivial   : 79
% 0.23/1.41  # Contextual simplify-reflections      : 0
% 0.23/1.41  # Paramodulations                      : 76
% 0.23/1.41  # Factorizations                       : 4
% 0.23/1.41  # Equation resolutions                 : 0
% 0.23/1.41  # Current number of processed clauses  : 14
% 0.23/1.41  #    Positive orientable unit clauses  : 2
% 0.23/1.41  #    Positive unorientable unit clauses: 1
% 0.23/1.41  #    Negative unit clauses             : 2
% 0.23/1.41  #    Non-unit-clauses                  : 9
% 0.23/1.41  # Current number of unprocessed clauses: 26
% 0.23/1.41  # ...number of literals in the above   : 65
% 0.23/1.41  # Current number of archived formulas  : 0
% 0.23/1.41  # Current number of archived clauses   : 16
% 0.23/1.41  # Clause-clause subsumption calls (NU) : 31
% 0.23/1.41  # Rec. Clause-clause subsumption calls : 28
% 0.23/1.41  # Non-unit clause-clause subsumptions  : 9
% 0.23/1.41  # Unit Clause-clause subsumption calls : 1
% 0.23/1.41  # Rewrite failures with RHS unbound    : 0
% 0.23/1.41  # BW rewrite match attempts            : 4
% 0.23/1.41  # BW rewrite match successes           : 4
% 0.23/1.41  # Condensation attempts                : 0
% 0.23/1.41  # Condensation successes               : 0
% 0.23/1.41  # Termbank termtop insertions          : 1480
% 0.23/1.41  
% 0.23/1.41  # -------------------------------------------------
% 0.23/1.41  # User time                : 0.015 s
% 0.23/1.41  # System time              : 0.002 s
% 0.23/1.41  # Total time               : 0.017 s
% 0.23/1.41  # Maximum resident set size: 2772 pages
%------------------------------------------------------------------------------