TSTP Solution File: SET183+3 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET183+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n023.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 00:49:55 EDT 2022

% Result   : Theorem 0.21s 1.39s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   30 (  12 unt;   0 def)
%            Number of atoms       :   70 (  13 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   66 (  26   ~;  25   |;   9   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   59 (   9 sgn  35   !;   0   ?)

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

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

fof(commutativity_of_intersection,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_of_intersection) ).

fof(intersection_is_subset,axiom,
    ! [X1,X2] : subset(intersection(X1,X2),X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersection_is_subset) ).

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

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(X1,X2)
       => intersection(X1,X2) = X1 ),
    inference(assume_negation,[status(cth)],[prove_subset_intersection]) ).

fof(c_0_7,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])])])])])])]) ).

fof(c_0_8,negated_conjecture,
    ( subset(esk1_0,esk2_0)
    & intersection(esk1_0,esk2_0) != esk1_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

fof(c_0_9,plain,
    ! [X4,X5,X6,X4,X5,X6] :
      ( ( member(X6,X4)
        | ~ member(X6,intersection(X4,X5)) )
      & ( member(X6,X5)
        | ~ member(X6,intersection(X4,X5)) )
      & ( ~ member(X6,X4)
        | ~ member(X6,X5)
        | member(X6,intersection(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)],[intersection_defn])])])])]) ).

cnf(c_0_10,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,negated_conjecture,
    subset(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    ( subset(X1,X2)
    | ~ member(esk3_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

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

cnf(c_0_14,negated_conjecture,
    ( member(X1,esk2_0)
    | ~ member(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,plain,
    ( subset(X1,X2)
    | member(esk3_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_16,plain,
    ( subset(X1,intersection(X2,X3))
    | ~ member(esk3_2(X1,intersection(X2,X3)),X3)
    | ~ member(esk3_2(X1,intersection(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    ( subset(esk1_0,X1)
    | member(esk3_2(esk1_0,X1),esk2_0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

fof(c_0_18,plain,
    ! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

fof(c_0_19,plain,
    ! [X3,X4] : subset(intersection(X3,X4),X3),
    inference(variable_rename,[status(thm)],[intersection_is_subset]) ).

fof(c_0_20,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])])])])]) ).

cnf(c_0_21,negated_conjecture,
    ( subset(esk1_0,intersection(X1,esk2_0))
    | ~ member(esk3_2(esk1_0,intersection(X1,esk2_0)),X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,plain,
    subset(intersection(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_24,negated_conjecture,
    intersection(esk1_0,esk2_0) != esk1_0,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_25,plain,
    ( X1 = X2
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_26,negated_conjecture,
    subset(esk1_0,intersection(esk2_0,esk1_0)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_15]),c_0_22]) ).

cnf(c_0_27,plain,
    subset(intersection(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_23,c_0_22]) ).

cnf(c_0_28,negated_conjecture,
    intersection(esk2_0,esk1_0) != esk1_0,
    inference(rw,[status(thm)],[c_0_24,c_0_22]) ).

cnf(c_0_29,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),c_0_28]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SET183+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12  % Command  : run_ET %s %d
% 0.11/0.33  % Computer : n023.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Sun Jul 10 22:19:40 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.21/1.39  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.21/1.39  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.21/1.39  # Preprocessing time       : 0.015 s
% 0.21/1.39  
% 0.21/1.39  # Proof found!
% 0.21/1.39  # SZS status Theorem
% 0.21/1.39  # SZS output start CNFRefutation
% See solution above
% 0.21/1.39  # Proof object total steps             : 30
% 0.21/1.39  # Proof object clause steps            : 17
% 0.21/1.39  # Proof object formula steps           : 13
% 0.21/1.39  # Proof object conjectures             : 11
% 0.21/1.39  # Proof object clause conjectures      : 8
% 0.21/1.39  # Proof object formula conjectures     : 3
% 0.21/1.39  # Proof object initial clauses used    : 9
% 0.21/1.39  # Proof object initial formulas used   : 6
% 0.21/1.39  # Proof object generating inferences   : 7
% 0.21/1.39  # Proof object simplifying inferences  : 5
% 0.21/1.39  # Training examples: 0 positive, 0 negative
% 0.21/1.39  # Parsed axioms                        : 8
% 0.21/1.39  # Removed by relevancy pruning/SinE    : 0
% 0.21/1.39  # Initial clauses                      : 18
% 0.21/1.39  # Removed in clause preprocessing      : 2
% 0.21/1.39  # Initial clauses in saturation        : 16
% 0.21/1.39  # Processed clauses                    : 307
% 0.21/1.39  # ...of these trivial                  : 15
% 0.21/1.39  # ...subsumed                          : 194
% 0.21/1.39  # ...remaining for further processing  : 98
% 0.21/1.39  # Other redundant clauses eliminated   : 2
% 0.21/1.39  # Clauses deleted for lack of memory   : 0
% 0.21/1.39  # Backward-subsumed                    : 0
% 0.21/1.39  # Backward-rewritten                   : 1
% 0.21/1.39  # Generated clauses                    : 687
% 0.21/1.39  # ...of the previous two non-trivial   : 647
% 0.21/1.39  # Contextual simplify-reflections      : 11
% 0.21/1.39  # Paramodulations                      : 671
% 0.21/1.39  # Factorizations                       : 14
% 0.21/1.39  # Equation resolutions                 : 2
% 0.21/1.39  # Current number of processed clauses  : 95
% 0.21/1.39  #    Positive orientable unit clauses  : 16
% 0.21/1.39  #    Positive unorientable unit clauses: 1
% 0.21/1.39  #    Negative unit clauses             : 1
% 0.21/1.39  #    Non-unit-clauses                  : 77
% 0.21/1.39  # Current number of unprocessed clauses: 356
% 0.21/1.39  # ...number of literals in the above   : 859
% 0.21/1.39  # Current number of archived formulas  : 0
% 0.21/1.39  # Current number of archived clauses   : 1
% 0.21/1.39  # Clause-clause subsumption calls (NU) : 2147
% 0.21/1.39  # Rec. Clause-clause subsumption calls : 2028
% 0.21/1.39  # Non-unit clause-clause subsumptions  : 205
% 0.21/1.39  # Unit Clause-clause subsumption calls : 47
% 0.21/1.39  # Rewrite failures with RHS unbound    : 0
% 0.21/1.39  # BW rewrite match attempts            : 9
% 0.21/1.39  # BW rewrite match successes           : 2
% 0.21/1.39  # Condensation attempts                : 0
% 0.21/1.39  # Condensation successes               : 0
% 0.21/1.39  # Termbank termtop insertions          : 9436
% 0.21/1.39  
% 0.21/1.39  # -------------------------------------------------
% 0.21/1.39  # User time                : 0.029 s
% 0.21/1.39  # System time              : 0.003 s
% 0.21/1.39  # Total time               : 0.032 s
% 0.21/1.39  # Maximum resident set size: 3292 pages
%------------------------------------------------------------------------------