TSTP Solution File: SET598+3 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n016.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 00:52:19 EDT 2022

% Result   : Theorem 0.28s 1.45s
% Output   : CNFRefutation 0.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   39 (  14 unt;   0 def)
%            Number of atoms       :  115 (  32 equ)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :  129 (  53   ~;  55   |;  15   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   46 (   4 sgn  29   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(prove_th57,conjecture,
    ! [X1,X2,X3] :
      ( X1 = intersection(X2,X3)
    <=> ( subset(X1,X2)
        & subset(X1,X3)
        & ! [X4] :
            ( ( subset(X4,X2)
              & subset(X4,X3) )
           => subset(X4,X1) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th57) ).

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

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

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

fof(intersection_of_subsets,axiom,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X1,X3) )
     => subset(X1,intersection(X2,X3)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersection_of_subsets) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( X1 = intersection(X2,X3)
      <=> ( subset(X1,X2)
          & subset(X1,X3)
          & ! [X4] :
              ( ( subset(X4,X2)
                & subset(X4,X3) )
             => subset(X4,X1) ) ) ),
    inference(assume_negation,[status(cth)],[prove_th57]) ).

fof(c_0_6,plain,
    ! [X3,X4] : subset(intersection(X3,X4),X3),
    inference(variable_rename,[status(thm)],[intersection_is_subset]) ).

fof(c_0_7,negated_conjecture,
    ! [X9] :
      ( ( subset(esk4_0,esk2_0)
        | ~ subset(esk1_0,esk2_0)
        | ~ subset(esk1_0,esk3_0)
        | esk1_0 != intersection(esk2_0,esk3_0) )
      & ( subset(esk4_0,esk3_0)
        | ~ subset(esk1_0,esk2_0)
        | ~ subset(esk1_0,esk3_0)
        | esk1_0 != intersection(esk2_0,esk3_0) )
      & ( ~ subset(esk4_0,esk1_0)
        | ~ subset(esk1_0,esk2_0)
        | ~ subset(esk1_0,esk3_0)
        | esk1_0 != intersection(esk2_0,esk3_0) )
      & ( subset(esk1_0,esk2_0)
        | esk1_0 = intersection(esk2_0,esk3_0) )
      & ( subset(esk1_0,esk3_0)
        | esk1_0 = intersection(esk2_0,esk3_0) )
      & ( ~ subset(X9,esk2_0)
        | ~ subset(X9,esk3_0)
        | subset(X9,esk1_0)
        | esk1_0 = intersection(esk2_0,esk3_0) ) ),
    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)],[c_0_5])])])])])])]) ).

fof(c_0_8,plain,
    ! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

cnf(c_0_9,plain,
    subset(intersection(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    ( esk1_0 = intersection(esk2_0,esk3_0)
    | subset(esk1_0,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_12,plain,
    ! [X3,X4,X3,X4] :
      ( ( subset(X3,X4)
        | X3 != X4 )
      & ( subset(X4,X3)
        | X3 != X4 )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])])]) ).

fof(c_0_13,plain,
    ! [X4,X5,X6] :
      ( ~ subset(X4,X5)
      | ~ subset(X4,X6)
      | subset(X4,intersection(X5,X6)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_of_subsets])]) ).

cnf(c_0_14,negated_conjecture,
    ( esk1_0 = intersection(esk2_0,esk3_0)
    | subset(X1,esk1_0)
    | ~ subset(X1,esk3_0)
    | ~ subset(X1,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_15,negated_conjecture,
    ( esk1_0 != intersection(esk2_0,esk3_0)
    | ~ subset(esk1_0,esk3_0)
    | ~ subset(esk1_0,esk2_0)
    | ~ subset(esk4_0,esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_16,negated_conjecture,
    subset(esk1_0,esk2_0),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_17,plain,
    subset(intersection(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_9,c_0_11]) ).

cnf(c_0_18,negated_conjecture,
    ( esk1_0 = intersection(esk2_0,esk3_0)
    | subset(esk1_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_19,plain,
    ( X1 = X2
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,plain,
    ( subset(X1,intersection(X2,X3))
    | ~ subset(X1,X3)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,negated_conjecture,
    ( intersection(esk2_0,esk3_0) = esk1_0
    | subset(intersection(esk2_0,X1),esk1_0)
    | ~ subset(intersection(esk2_0,X1),esk3_0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_9]) ).

cnf(c_0_22,negated_conjecture,
    ( subset(esk4_0,esk3_0)
    | esk1_0 != intersection(esk2_0,esk3_0)
    | ~ subset(esk1_0,esk3_0)
    | ~ subset(esk1_0,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_23,negated_conjecture,
    ( subset(esk4_0,esk2_0)
    | esk1_0 != intersection(esk2_0,esk3_0)
    | ~ subset(esk1_0,esk3_0)
    | ~ subset(esk1_0,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_24,negated_conjecture,
    ( intersection(esk2_0,esk3_0) != esk1_0
    | ~ subset(esk1_0,esk3_0)
    | ~ subset(esk4_0,esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).

cnf(c_0_25,negated_conjecture,
    subset(esk1_0,esk3_0),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_26,plain,
    ( intersection(X1,X2) = X3
    | ~ subset(intersection(X1,X2),X3)
    | ~ subset(X3,X2)
    | ~ subset(X3,X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_27,negated_conjecture,
    ( intersection(esk2_0,esk3_0) = esk1_0
    | subset(intersection(esk2_0,esk3_0),esk1_0) ),
    inference(spm,[status(thm)],[c_0_21,c_0_17]) ).

cnf(c_0_28,negated_conjecture,
    ( subset(esk4_0,esk3_0)
    | intersection(esk2_0,esk3_0) != esk1_0
    | ~ subset(esk1_0,esk3_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_16])]) ).

cnf(c_0_29,negated_conjecture,
    ( subset(esk4_0,esk2_0)
    | intersection(esk2_0,esk3_0) != esk1_0
    | ~ subset(esk1_0,esk3_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_16])]) ).

cnf(c_0_30,negated_conjecture,
    ( intersection(esk2_0,esk3_0) != esk1_0
    | ~ subset(esk4_0,esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).

cnf(c_0_31,negated_conjecture,
    intersection(esk2_0,esk3_0) = esk1_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_25]),c_0_16])]) ).

cnf(c_0_32,negated_conjecture,
    ( subset(esk4_0,esk3_0)
    | intersection(esk2_0,esk3_0) != esk1_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_25])]) ).

cnf(c_0_33,negated_conjecture,
    ( subset(esk4_0,esk2_0)
    | intersection(esk2_0,esk3_0) != esk1_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_25])]) ).

cnf(c_0_34,negated_conjecture,
    ~ subset(esk4_0,esk1_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).

cnf(c_0_35,negated_conjecture,
    ( subset(X1,esk1_0)
    | ~ subset(X1,esk3_0)
    | ~ subset(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_20,c_0_31]) ).

cnf(c_0_36,negated_conjecture,
    subset(esk4_0,esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_31])]) ).

cnf(c_0_37,negated_conjecture,
    subset(esk4_0,esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_31])]) ).

cnf(c_0_38,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.15  % Command  : run_ET %s %d
% 0.15/0.36  % Computer : n016.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Mon Jul 11 09:04:57 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.28/1.45  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.28/1.45  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.28/1.45  # Preprocessing time       : 0.015 s
% 0.28/1.45  
% 0.28/1.45  # Proof found!
% 0.28/1.45  # SZS status Theorem
% 0.28/1.45  # SZS output start CNFRefutation
% See solution above
% 0.28/1.45  # Proof object total steps             : 39
% 0.28/1.45  # Proof object clause steps            : 28
% 0.28/1.45  # Proof object formula steps           : 11
% 0.28/1.45  # Proof object conjectures             : 25
% 0.28/1.45  # Proof object clause conjectures      : 22
% 0.28/1.45  # Proof object formula conjectures     : 3
% 0.28/1.45  # Proof object initial clauses used    : 10
% 0.28/1.45  # Proof object initial formulas used   : 5
% 0.28/1.45  # Proof object generating inferences   : 9
% 0.28/1.45  # Proof object simplifying inferences  : 24
% 0.28/1.45  # Training examples: 0 positive, 0 negative
% 0.28/1.45  # Parsed axioms                        : 9
% 0.28/1.45  # Removed by relevancy pruning/SinE    : 3
% 0.28/1.45  # Initial clauses                      : 13
% 0.28/1.45  # Removed in clause preprocessing      : 0
% 0.28/1.45  # Initial clauses in saturation        : 13
% 0.28/1.45  # Processed clauses                    : 43
% 0.28/1.45  # ...of these trivial                  : 3
% 0.28/1.45  # ...subsumed                          : 1
% 0.28/1.45  # ...remaining for further processing  : 39
% 0.28/1.45  # Other redundant clauses eliminated   : 2
% 0.28/1.45  # Clauses deleted for lack of memory   : 0
% 0.28/1.45  # Backward-subsumed                    : 2
% 0.28/1.45  # Backward-rewritten                   : 16
% 0.28/1.45  # Generated clauses                    : 80
% 0.28/1.45  # ...of the previous two non-trivial   : 63
% 0.28/1.45  # Contextual simplify-reflections      : 0
% 0.28/1.45  # Paramodulations                      : 78
% 0.28/1.45  # Factorizations                       : 0
% 0.28/1.45  # Equation resolutions                 : 2
% 0.28/1.45  # Current number of processed clauses  : 19
% 0.28/1.45  #    Positive orientable unit clauses  : 8
% 0.28/1.45  #    Positive unorientable unit clauses: 1
% 0.28/1.45  #    Negative unit clauses             : 1
% 0.28/1.45  #    Non-unit-clauses                  : 9
% 0.28/1.45  # Current number of unprocessed clauses: 19
% 0.28/1.45  # ...number of literals in the above   : 54
% 0.28/1.45  # Current number of archived formulas  : 0
% 0.28/1.45  # Current number of archived clauses   : 18
% 0.28/1.45  # Clause-clause subsumption calls (NU) : 53
% 0.28/1.45  # Rec. Clause-clause subsumption calls : 35
% 0.28/1.45  # Non-unit clause-clause subsumptions  : 2
% 0.28/1.45  # Unit Clause-clause subsumption calls : 13
% 0.28/1.45  # Rewrite failures with RHS unbound    : 0
% 0.28/1.45  # BW rewrite match attempts            : 11
% 0.28/1.45  # BW rewrite match successes           : 7
% 0.28/1.45  # Condensation attempts                : 0
% 0.28/1.45  # Condensation successes               : 0
% 0.28/1.45  # Termbank termtop insertions          : 1636
% 0.28/1.45  
% 0.28/1.45  # -------------------------------------------------
% 0.28/1.45  # User time                : 0.015 s
% 0.28/1.45  # System time              : 0.003 s
% 0.28/1.45  # Total time               : 0.018 s
% 0.28/1.45  # Maximum resident set size: 2768 pages
%------------------------------------------------------------------------------